Whenever the subject of deals involving recognizable names is broached in May, the response is standard across baseball:

“Nothing really happens until the draft is over,’’ is the canned phrase throughout the AL and NL.

That doesn’t mean the swapping will immediately begin at tomorrow’s conclusion of the final round of the MLB draft.

But now that general managers and scouts are no longer involved with high school and college work, their energy and focus will be on the professional level.

“It’s always hard to predict [when the trade market will start],’’ Yankees GM Brian Cashman said from Tampa, where he is involved in the draft that started Thursday night, continues Friday and ends Saturday after 40 rounds. “Last year there was a lot of movement before the [July 31 trading] deadline. But no one really talks about trades until after the draft.’’

Cashman made several low-level deals before the draft. He got Chris Nelson (since gone) and Reid Brignac from Colorado, David Huff (currently at Triple-A) from the Indians and Alberto Gonzalez (at Triple-A) from the Cubs.

Since the middle of spring training, the Yankees’ roster has been fluid. Ben Francisco was brought in to play left field against left-handed hurlers. Vernon Wells essentially replaced Francisco, who has been released. Lyle Overbay surfaced during the final week of spring training and was the starting first baseman for two months.

Now Cashman and his scouts will look at what’s available to bolster a club that started last night’s game against the woeful Mariners at Safeco Field 1 1/2 games behind the first-place Red Sox in the AL East and riding a three-game winning streak after dropping seven of the previous eight.

Or there could come a time when the Yankees fall out of postseason contention and look to move players who don’t figure in their plans next year.

Two who fit that profile are reliever Joba Chamberlain and starter Phil Hughes. They are going to be free agents following the season and neither is a strong candidate to return.

Chamberlain will find interest in the free-agent market, possibly with a team offering him a chance to close. That role with the Yankees will fall to David Robertson next year when Mariano Rivera is gone.