MGM and Caesars Entertainment think they may be a pair.

MGM has hired investment bank Morgan Stanley and law firm Weil, Gotshal & Manges to start studying the idea of the giant tie-up, a gaming source close to the situation said.

No offer is on the table, though, according to sources.

Activist hedge funds, which together own about a 25 percent chunk of underperforming Caesars, have been pushing for an MGM deal, sources said. Caesars shares are off 25 percent year to date, while MGM is down 15 percent.

These funds, including Canyon Partners, which holds leading stakes in both companies, were seen to be behind the ouster of Caesars boss Mark Frissora, who announced last week he was resigning as of Feb. 8.

“Everyone knows that without a CEO, Caesars is in play,” a source with direct knowledge of the situation said.

Chaney Sheffield, an ex-Morgan Stanley investment banker who heads Canyon’s lodging and gaming investments, is reportedly pushing a casino colossus — in part to save money on overhead and marketing, the source added.

“I think the next three to four months will be fascinating,” a second gaming source close to the situation said.

If combined, MGM and Caesars would own about half the hotel rooms in Las Vegas and Atlantic City. Such an intense concentration could raise regulatory concerns in both states.

MGM’s enterprise value, equity plus debt, is $30 billion, and Caesars’ chips stand at $22 billion.

Caesars recently rejected a takeover offer from Tilman Fertitta’s much smaller Golden Nugget casino chain.

That scenario is seen as playbook perfect for the activist hedgies, with larger MGM playing a white knight role, sources said.

MGM may not be the only game in town, though, for Caesars.

Wynn Resorts, at $18 billion enterprise value, may sidle up to the table if it gets to keep its license to build a Boston-area casino, sources said.

Malaysia’s Genting Group, which owns Resorts World at Aqueduct Racetrack, could also be in the mix, as well as private equity firms that have a license to operate casinos, like The Blackstone Group, sources said.

Caesars also is in negotiations to buy some of Jack Entertainment’s Ohio casinos, but tax implications may undo that effort, a source said.

MGM and Caesars declined to comment, and Canyon declined comment beyond saying it had not signed a confidentiality agreement with MGM.