MINNEAPOLIS -- The Twins extended a qualifying offer to right-hander Jake Odorizzi, the club announced Monday, but did not extend one to Kyle Gibson or Michael Pineda. Odorizzi has 10 days to accept or reject the offer, which is a one-year deal valued at $17.8 million for the 2020 season.

After working on his mechanics at the Florida Baseball Ranch last offseason, Odorizzi rebounded from a shaky 2018 to post some of the best numbers of his career in '19, when he pitched to a 3.51 ERA with a career-high 178 strikeouts in 159 innings. He was named to the American League All-Star team for the first time in his eight-year career.

With Odorizzi coming off such a successful season in his walk year, the right-hander could opt to test the market in pursuit of a multiyear contract. If Odorizzi were to reject the qualifying offer to enter free agency, the Twins would receive a compensatory Draft pick for his departure.

But if the 29-year-old Odorizzi thinks that he could still improve his stock with another year in Minnesota, he could accept the qualifying offer to receive a guaranteed salary while hoping to carry his success into a second straight season, which could position him for a multiyear deal next offseason.

"I really enjoyed my two years here, and I think I’ve been pretty straightforward about that," Odorizzi said after the Twins' season ended in the American League Division Series. "I try to be as straightforward as possible with just about everything. That’s just the kind of person I am, and if I’m back, that would be great. I've really taken a liking to here. If not, I wish nothing but the best for everybody. This is a great group, top to bottom."

In the past, it would likely have been an easier call for Odorizzi to reject the offer and test the open market. In fact, since the qualifying offer system was implemented in 2012, only six of the 80 players that have received an offer have accepted. But given the current state of free agency, in which former Cy Young Award winner Dallas Keuchel was left without a team until June after rejecting a qualifying offer last offseason, Odorizzi and his representatives may think twice about testing the waters.

Odorizzi made $9.5 million in 2019, his final season of arbitration eligibility.

The Twins appear to be in decent position regardless of Odorizzi's decision. If he were to accept the offer, the Twins would have one fewer rotation spot to fill for 2020, and one of their most consistent starters would return to help resolve one question mark on a playoff-hopeful team in need of lots of help on the pitching staff.

Pineda was not extended the qualifying offer despite also serving as one of the Twins' most consistent rotation options in 2019. After a difficult April, Pineda posted a 3.46 ERA from May through the end of his season, which was cut short by a suspension due to a violation of the Joint Drug Prevention and Treatment Program. Pineda still has 39 games of his suspension to serve to begin the 2020 campaign.

Though Gibson might have been positioned for a qualifying offer if he had carried the success of his breakout 2018 into this year, he instead regressed to a 4.84 ERA due to a season-long battle with ulcerative colitis. The underperformance and health uncertainty made it unlikely that the 32-year-old Gibson, the longest-tenured member of the Twins, would receive the $17.8 million commitment.

Twins decline Pérez's option for 2020

The Twins announced Monday that they declined their $7.5 million club option for starter Martin Pérez, making the 28-year-old southpaw a free agent and committing the Twins to rebuilding a full four-fifths of their starting rotation this offseason.

Pérez was acquired last offseason to serve as the Twins' fifth starter on a one-year, $4 million deal with a club option for 2020, and posted a 5.12 ERA in 32 appearances (29 starts) with 135 strikeouts in 165 1/3 frames. The Twins chose to exercise a $500,000 buyout instead of committing $7.5 million to bring him back to Target Field next season.

The club's only other option decision for 2020 involved designated hitter Nelson Cruz, and it came as no surprise at all that the veteran's $12 million club option was officially exercised on Monday, as had been previously reported in October.

The Twins' pitching brain trust had Pérez in mind because they felt there were elements of his mechanics and pitch usage that could be improved from the left-hander's seven seasons with the Rangers. And indeed, he relied less on his sinker and added a new cutter to his arsenal while seeing the average velocity of his four-seam fastball rise by 1.4 mph.

The Pérez project initially proved successful, as he posted a 2.89 ERA through his first 10 appearances, but his 6.27 ERA in the second half resulted in a difficult finish to the season that also saw the veteran left-hander left off the Twins' roster for the ALDS against the Yankees.

Other moves

• Left-handed pitcher Stephen Gonsalves was claimed off waivers by the Mets on Monday. Gonsalves is a former fourth-round selection in the 2013 MLB Draft who was ranked by MLB Pipeline as the No. 18 prospect in the Twins' organization. He made his Major League debut in 2018 and pitched to a 6.57 ERA in 24 2/3 innings but was limited to eight Minor League games in 2019 as he dealt with a left elbow injury.

• Right-hander Kohl Stewart was outrighted off the 40-man roster and elected free agency. Stewart, 25, was a first-round selection in the 2013 MLB Draft and debuted for the Twins in 2018. He had a 4.79 ERA in 17 games over parts of two seasons with the Twins. Minnesota's 40-man roster is now at 31.