Mike Celizic

Other than their annual interleague Subway Series, the Mets and the Yankees don’t often compete with one another in anything other than for the top headline on the back pages of the city’s notorious tabloids. Their fan bases do not overlap. The Yankees are the Bronx and the establishment. The Mets are Queens and the underdogs. The Yankees are Wall Street and Broadway. The Mets are the Cross Island Parkway.

Normally, the two teams don’t even compete for free agents, the Yankees preferring products off the top shelf and the Mets being more cautious with their money. But that could change this year with baseball’s free-agent signing period being in full swing.

If they end up bidding for the same player, it’s most likely to be starting pitcher Derek Lowe. The Yankees should look at the durable and reliable Lowe as their second free-agent starter after CC Sabathia — if Sabathia decides money is more important than the happiness of playing on the West Coast. The Mets will probably feel the same way about Lowe to fill the starting slot vacated by free agent Pedro Martinez.

That’s a shame, because both teams need a big upgrade in left field and it would be a lot more fun if they were to do battle over Manny Ramirez, who grew up in New York. Unfortunately for the headline writers and talk show hosts, neither team seems to be interested in the best right-handed hitter in the game not named Albert Pujols.

The lack of interest is somewhat mystifying. With the Yankees, even Manny’s erratic defensive skills would be an upgrade over a battered and aging Hideki Matsui and Johnny Damon, whose arm is shot.

The Mets desperately needs a powerful right-handed bat in a lineup that’s got too many lefties in it. They also need someone who, unlike David Wright, can get a runner home from third in late-inning pressure situations. The team also needs a left fielder. The plan seems to be to platoon Daniel Murphy and Fernando Tatis while waiting for the 20-year-old Fernando Martinez — a crown jewel of the Mets farm system — to be ready for the big time, which could happen as early as next summer.

As good as Martinez might become, he’s still just a kid — and an often-injured one at that. If he’s really good, the Mets can find a place for him. But in the meantime, if you can get Ramirez, why wouldn’t you try?

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Money shouldn’t be an issue for either team. Both are opening new stadiums that figure to be packed from opening day to season’s end. Both have their own television networks that bring in more revenue.

There is the issue of Manny’s occasional pouts and attention lapses, a problem that could become a major issue if the local media turns on him. But when you look back over Manny’s career, his production far outweighs his occasional forays into Manny Land.

But the Yankees, who almost never pass up a superstar free agent, don’t want him and the Mets don’t feel they need him.

Instead, the Yankees may pursue Mark Teixeira, the Angels great power-hitting first baseman. And if they don’t, they should, because the Bronx Bombers are letting Bobby Abreu walk and need a big bat in the middle of the lineup to protect Alex Rodriguez and to produce in the clutch. The Yankees earlier traded for the White Sox’s Nick Swisher, who can play first as well as the outfield. He could end up in left with Xavier Nady in right.