ST. LOUIS — It's Jose Berrios' turn to pitch Friday night. Which is why Griffin Jax flew to Missouri on Thursday.

Jax, technically still a member of the St. Paul Saints, will presumably start the opener of a three-game series with the Cardinals for the Twins if Berrios, one of the most sought-after players on MLB's robust trade market, is dealt to a contender before Friday's 3 p.m. deadline — a prospect that grows more likely as more teams enter the bidding.

The Blue Jays and Rays, according to major league sources with knowledge of the Twins' maneuvering, have joined three NL West teams and, according to an MLB Network report, the Red Sox and Mariners as serious competitors for the two-time All-Star. The Twins are also trying to interest some of those suitors in a less costly alternative — Michael Pineda — as the scramble for championship-caliber upgrades intensifies.

The Twins might benefit from the back-and-forth bidding that broke out Thursday between the Padres and Dodgers over three-time Cy Young winner Max Scherzer. Berrios is widely considered the second-best pitcher available this week, and San Diego, which lost out on Scherzer to the Dodgers, figures to be motivated to make another upgrade to answer its rival.

But the Rays, who already pulled off a trade with Minnesota last week for Nelson Cruz, have plenty of motivation as well. Last year's AL champions are two games behind Boston in the AL East, and have already been swapping relievers in order to bolster their bullpen for the postseason. Tampa Bay acquired former Twin JT Chargois from the Mariners on Thursday.

The Blue Jays' lack of depth behind an otherwise solid rotation has been exposed with rookie righthander Alek Manoah on the injured list, making one of the Twins' options particularly appealing right now. The Rays, Blue Jays, Padres and Mariners are all ranked among the most loaded minor league organizations right now, making them ideal trading partners.

With a career-best 3.48 ERA and 1.044 WHIP this season, Berrios has been a standout on an especially subpar pitching staff this season. The Twins (5.01) and Orioles (5.48) are the only AL teams with ERAs above 5.00. Pineda owned a 2.62 ERA as the season passed Memorial Day, and though he's been beset by forearm issues since then, has allowed only three runs in his last two starts.

Pineda's contract, however, expires this fall, and though Berrios cannot become a free agent until after the 2022 season, he has said he will seek a market-value contract that figures to reach more than $100 million. His value in a trade may never be higher.

Other rumored deals seem to have been undone by alternate moves, such as a discussion between the Twins and Yankees over outfielder Max Kepler. New York reached an agreement with Texas to acquire a different left-handed outfielder, Joey Gallo, likely dousing any chance of that deal being worked out.