ESPN New York, which first reported the contract talks, indicated that the extension will be comparable to the five-year, $28.5 million deal that Rangers left-hander Derek Holland signed last month. Holland's deal included two team options, for $11 million and $11.5 million.
Niese did not respond to a message seeking comment. The Mets also have not commented on the negotiations.
Niese, who is arbitration-eligible for the first time after this season and can become a free agent after the 2015 season, finished 11-11 with a 4.40 ERA last year, missing the final month of the season with a right intercostal strain. One of three homegrown Mets in the Opening Day rotation, he is 22-23 over 65 career appearances with the Mets, with a 4.39 ERA.
Both sources said that the Mets have been in talks with Niese since the beginning of Spring Training, though one noted that "we're not in the home stretch."
At the behest of former teammate Carlos Beltran, Niese underwent a rhinoplasty operation in October to reconstruct the bone structure in his nose. The left-hander credited that operation for allowing him to breathe more freely and improve his offseason conditioning program.