NEW YORK -- The other day, one Yankees person neatly summed up their offense in four words.

“Our offense is offensive.’’

So when the Yankees say they are “open for business,’’ as general manager Brian Cashman said the other day, it’s clear what they’re seeking from the trade market: hitters.

The makeshift lineup that had surprised so many folks for two months and kept them afloat has turned into a pumpkin in June, when the Yankees have scored the second fewest runs (54) in baseball and posted the worst OPS (.591). Not very Yankee-like.

However, in looking for offense, Cashman is confronted with a few issues.

One is that it’s still hard to know which of the many injured players are going to make it back, and when. Except perhaps Mark Teixeira, whose timetable is listed as “TBD’’ on Yankees.com, they are all at least a few weeks away, and already there have been surprises and setbacks throughout.

Should he seek a third baseman (Alex Rodriguez’s rehab is said to be going “fantastic’’), a shortstop, an outfielder or something else?

A second issue is that the Yankees, for now at least, haven’t given up hope of getting the payroll down below $189 million for 2014, which means they’ll likely shy away from folks on big long-term deals.

Yet another issue -- and this is the big one -- is that the hitting market looks less than great. The best hitters are largely on the better teams, and thus not going anywhere.

While the Yankees are “open’’ to do business, there’s no proof anything serious is taking place yet. But here are a few names to keep in mind, names that could possibly hit the market and help in varying degrees.

1.Giancarlo Stanton, Marlins OF. Probably a pipe dream. There’s no evidence that the Marlins will even entertain offers, and if they do, other teams, including the Rangers, who also have a need, are better equipped to pull off such a monster move. Doesn’t hurt to dream, though.

2.  Alex Rios, White Sox OF. Terrific two-way player has proved to be worth the surprise waiver pickup from a few years back. He has 12 homers, 12 steals and can play all three outfield positions. The White Sox will consider dealing him if they can’t turn it around.

3. Chase Headley, Padres 3B. Even before the Padres went on a nice run to put themselves into the thick of the NL West race, they showed no real desire to deal Headley. Should they change their minds, the Yankees surely would love to have him.

4. Alfonso Soriano, Cubs OF. There have been rumors for years, almost since they traded him for A-Rod, that the Yankees might consider trying to get him back. One big issue is that while the Cubs are willing to pay the vast majority of his $18 million salary this year and next, they’d insist on a good prospect back for him.

5.  Aramis Ramirez, Brewers 3B. There seems to be a split among Brewers people over how eager they should be to sell, but Ramirez is making $13 million, and they already acquired a potential replacement in Juan Francisco. Probably not a real consideration for the Yankees yet since A-Rod appears to be working his way back.

6.  Kendrys Morales, Mariners 1B/DH. The switch hitter is a free agent at year’s end. A professional hitter who’s doing better -- a lot better -- than most do in Seattle. Has eight homers, 37 RBI and a .276 batting average.

7.  Michael Young, Phillies 3B. A professional hitter and good clubhouse guy. But as with A-Ram, the Yankees would want to see if A-Rod makes it back first.

8. Michael Morse, Mariners OF/1B. He has considerable power and, like Morales, he is in the last year of his Mariners contract.

9.  Josh Willingham, Twins OF. He has slumped a bit this year but has generally overcome playing in deep pitchers’ parks (Oakland Coliseum, Target Field) the past few years. Definite power threat.

10.  Justin Morneau, Twins 1B. He just broke out of a long homer slump, cracking his third dinger of the season to tie Kirby Puckett on the all-time Twins list. But he, too, is a professional hitter.

11.  Matt Adams, Cardinals 1B. There’s no great reason the Cardinals would trade him, other than that they have so many good players they’ve only found 80 at-bats for this burgeoning slugger so far. Would be quite a coup. Unlikely.