MINNEAPOLIS — The Tigers and Blue Jays are attached to the Yankees’ minor league system with a week to go before the trade deadline.

While the asking price for Tigers starter Matthew Boyd might be too high for the Yankees, right-handed reliever Shane Greene, a former Yankee, is expected to be dealt and the Yankees have been shopping for bullpen help, too.

The Tigers had a scout following Double-A Trenton for the past week and will go with the Thunder to Erie. Right-hander Deivi Garcia is considered by some organizations to be the Yankees’ top-overall prospect, so it’s not likely the Yankees would deal him straight up for Greene, a 30-year-old who will be a free agent after the 2020 season.

The Blue Jays, who are openly shopping right-handed starter and Medford, NY, native Marcus Stroman, have scouts scouring the lower levels of the Yankees’ system.

In 37 games for the pitiful Tigers this season, Greene has 22 saves and a 1.22 ERA. He saved 32 last year but with a 5.12 ERA.

Stroman, a free agent after the 2020 season, is 6-11 with a 2.96 ERA in 21 starts for the woeful Jays.

Greene, a 15th-round pick of the Yankees in the 2009 draft, appeared in 15 games (14 starts) for the 2014 Yankees and went 5-4 with a 3.78 ERA. On Dec. 5 of that year, Greene was sent to the Tigers in a three-way deal that included Arizona and brought Didi Gregorius to the Yankees. Robbie Ray, a lefty starter with the Diamondbacks, went from the Tigers to Arizona in that trade. Ray also has been on the Yankees’ radar.

Brett Gardner missed his fourth straight game because of a sore left knee that he put through agility drills before Wednesday night’s game.

Gardner and Aaron Boone talked on the field and it appeared to be animated.

“We were just talking about how I am feeling and trying to be smart. Obviously, after four days out of the lineup, want to make sure we don’t take any steps backward,’’ said Gardner, who started feeling discomfort in the hinge about a week ago and aggravated it making a diving catch Saturday at Yankee Stadium. He was scratched from the lineup the next day and hasn’t played since.

Mike Tauchman, who hit .563 (9-for-16) with a 1.486 OPS in the previous five games, started in left field for the sixth straight game. He stayed red-hot, going 2-for-4 with a two-run triple.

Gardner said he was hopeful to play Thursday night.

There is a chance Dellin Betances stretches his throwing program to 90 feet for the first time Thursday in Boston.