(Corrects price of Legendary Entertainment acquisition to $3.5 billion)

By Greg Roumeliotis

July 14 (Reuters) - AMC Entertainment Holdings is exploring a potential sweetened bid for Carmike Cinemas Inc that would top its previous $1.1 billion offer for the smaller movie theater chain, according to a person familiar with the matter.

Any price increase will likely be incremental and the company could still decide to walk away, the person added, asking not to be named because the matter is confidential.

Carmike declined to comment while AMC, which is majority-owned by Chinese billionaire Wang Jianlin's Dalian Wanda Group, could not be reached for comment.

Carmike said on Thursday that it will continue to have ongoing discussions with AMC after it delayed a July 15 shareholder vote on AMC's previous $30 per share offer.

It was the second time that Carmike postponed the vote, which is now set for July 25.

AMC's chief executive Adam Aron, speaking in reference to an analyst's question on a conference call earlier this week, said it was "accurate" that AMC could add some stock to its cash deal with Carmike as it looks to decrease its leverage.

AMC is aiming to become the No. 1 U.S. movie theater chain through the acquisition.

Aron has been vocal about not wanting to overpay for Carmike and has said the deal faced "considerable risk." Many Carmike shareholders, including top holder Mittleman Brothers along with Driehaus Capital Management, have resisted the current deal.

Earlier this week, AMC said it would buy London-based Odeon & UCI Cinemas Group from Guy Hands' private equity firm Terra Firma in a deal valued at about 921 million pounds ($1.21 billion).

Wanda, a Chinese real estate conglomerate, bought movie studio Legendary Entertainment earlier this year for $3.5 billion. It is also looking at buying a stake in Viacom Inc's Paramount Pictures, Reuters reported.

(Reporting by Greg Roumeliotis in New York; additional reporting by Liana B. Baker in San Francisco; Editing by Andrew Hay)