Two years after one of the best seasons in A’s franchise history, Blake Treinen is on the trading block — and if he isn’t moved by 5 p.m. Monday, indications are that the team will choose not to tender him a contract for 2020.

That notion would have been unthinkable a year ago, when Treinen was coming off a 2018 All-Star season in which he had put up an 0.78 ERA, the lowest in major-league history by a pitcher with a minimum of 80 innings.

In 2019, however, Treinen never got on track. His sinker, so impressive the previous season, was not as effective — there was even thought the new baseball might have played a role. He lost his closer job to Liam Hendriks and finished with a a 4.91 ERA, walking 37 batters and allowing nine homers in 58 ⅔ innings after walking just 21 and giving up two homers in 80 ⅓ innings the year before. Opponents hit .257 in 2019 after just .158 in 2018.

Treinen earned $6.4 million this past season, and he could wind up close to the $8 million mark in arbitration. Given his superb 2018, there could be some teams willing to take a flier on him either via a trade or as a free agent, but the A’s budget concerns make the 31-year-old, a free agent after 2020, a prime non-tender candidate.

Oakland’s other obvious non-tender/trade possibility is second baseman Jurickson Profar, who after coming over from Texas in a three-way deal last winter also endured a disappointing season, batting .218 and developing major throwing difficulties.

He improved toward the end of the season and is only 26 so his status as one of baseball’s top prospects earlier in the decade might pique some interest. But he could wind up making $6 million — likely too much for the numbers he had last season. The right-handed-heavy A’s would like more left-handed hitters in their lineup and he’s a switch hitter, but that’s probably not enough of a reason to make Profar one of the team’s higher-paid position players.

With left-handed specialists losing some value next season following the implementation of a rule that requires pitchers to face at least three hitters (or finish an inning), Oakland might consider non-tendering lefty Ryan Buchter. However, only 23 of Buchter’s 64 appearances were one- or two-batter outings, and he made nine multi-inning appearances. And while the A’s are looking for a left-handed hitting catcher, non-tendering Josh Phegley seems unlikely; he’s set to make just over $2 million in arbitration projections.

Non-tendering a player does not prohibit a team from re-signing that player at a potential savings; the A’s non-tendered starter Mike Fiers last year, then brought him back the next month on a two-year deal worth $14 million. Oakland also will be keeping a close eye on other teams’ transactions leading up to next week’s winter meetings in the event some intriguing names are non-tendered.

Susan Slusser is a San Francisco Chronicle staff writer. Email: sslusser@sfchronicle.com Twitter: @susanslusser