DALLAS (AP) _ Ailing First RepublicBank Corp. may have to divest itself of some of its banks to become more attractive to investors, experts say.

First RepublicBank, weakened by a run on deposits and recent multimillion- dol lar losses, received a $1 billion injection of capital last week from the Federal Deposit Insurance Corp.

But because it could take as much as $5 billion to rescue the nation's 13th-largest bank holding company, banking regulators are considering selling First RepublicBank's individual operations as a marketing alternative.

FDIC Chairman L. William Seidman said such a move ''certainly is an option.''

No spokesman for FirstRepublic Bank was available Tuesday to comment on the idea.

''The first thing you think of is splitting the company into bite-size morsels,'' said James Sexton, a former FDIC director of supervision who is a consultant at Bracewell & Patterson, an Austin, Texas law firm.

The holding company's banks in major markets could be packaged together or in regional or in statewide combinations, analysts said. The holding company has banks in Dallas, Austin, Houston and San Antonio.

''It's a very large bank for someone else to acquire,'' said Tanya Azarchs, a banking analyst with New York-based Standard & Poor's Corp. ''I don't see anyone on the scene that's willing to do that.''

Although the breakup of the holding company could make it more accessible to investors, some argue it would be better if the company remained intact.

''These banks are intertwined, having common management, borrowers and computer systems,'' Sexton said. ''Breaking off chunks presents some tough administrative problems.''

The bank holding company already is consolidating some of its banks, which could make a breakup more difficult. First RepublicBank already has cut the number of banks from 103 to 73, and plans to consolidate until only 40 banks are left.

First RepublicBank reported a 1987 loss of $656.8 million, $3.92 billion in problem assets and had deposit outflows of more than $2 billion this year. Its assets total about $33.2 billion.