I’d just finished my 50th lap in the Equinox pool when somebody jumped into my lane.

It turned out to be John Slattery, the “silver fox,” as my girlfriend calls him — Roger Sterling of “Mad Men.” I’ve never seen the show — I’m still catching up on “St. Elsewhere” — but I’ve been a fan of Slattery’s ever since I saw him in a superb production of Harold Pinter’s “Betrayal” at the Roundabout in 2000.

His co-stars, by the way, were Juliette Binoche and a then-unknown Liev Schreiber. All were terrific.

Slattery and I exchanged pleasantries — “Do you mind if we share the lane?” — before I asked him what he’ll do now that “Mad Men” has finished shooting its final season. (I didn’t say, “Now that you’re famous, you would certainly be in demand on the Great White Way,” but, well, he is, on both counts.)

“I am looking for a play,” he said.

Proper actor that he is, he wants to be on stage again.

I told him if a good play comes my way, I’d send it along.

And then an idea occurred to me. Since Broadway’s so star-driven, why not pair him with Jon Hamm?

A 14-week engagement in a play starring the men from “Mad Men” would sell out faster than, well, Hugh Jackman.

I mentioned this to a couple of Broadway producers the other night at a cocktail party. I won’t mention their names (it was an off-the-record event), but let me describe the exchange:

Me: “I saw John Slattery in the pool the other day and he said he wants to do a play. Why don’t you guys come up with something for him and Jon Hamm to do together?”

Producer X, who was wearing a turtleneck, fell backward: “Oh, my God, I would do that in a second.”

Producer Y, wearing a very fetching necklace, said: “That is a brilliant idea!”

And then, I kid you not, they nearly scratched each other’s eyes out vying for the idea.

Producer Y said, “I was here when you talked about it! You have to cut me in!”

Producer X said, “I will, I will. We’ll do it together.”

We’ll see about that. This is a business where the only currency is betrayal. But let the record show, before the agents get involved, that this was my idea, inspired by 50 laps in a pool.

I’m told the wheels are already in motion. Producers X and Y are making calls, agents for Hamm and Slattery are fielding them.

So let me suggest a few plays they might do:

“The Front Page,” that great comedy about the newspaper business, when newspapers mattered.

“Once in a Lifetime,” the still-sharp satire of Hollywood by George S. Kaufman and Moss Hart.

I’d like to suggest a David Mamet play here — “Glengarry Glen Ross” — but that’s obvious. And, frankly, the Mamet plays have been done to death, and they’re starting to show their age.

How about something obscure? Peter Nichols’ “Passion Play,” a brilliant drama about adultery and betrayal. Perfect, it seems to me, for these “Mad Men.”

But readers, if you have better ideas, send them along and I’ll pass them on to John Slattery, the next time I see him at the swim meet.