Newsday is reporting that negotiations began a little more than a week ago with a meeting between Tellem and general manager Brian Cashman.
Mussina prefers to stay a Yankee and, according to the report, is willing to accept a smaller salary.
"Everything's going fine," Mussina told the Newark Star-Ledger. "We're getting there. I'm confident we'll work something out."
Mussina is coming off a six-year, $88.5-million contract. The expiring contract included a $17-million team option for next year; the Yankees have until Nov. 15 to decline it and pay a $1.5-million buyout.
Mussina's contract, which is expected to be worth as much as $25 million, could be finalized sometime this week.
According to Newsday, the Yankees also will officially pick up
Gary Sheffield's $13-million option before Sunday night's deadline, still with the intention of trading him to the highest bidder. Cashman declined to comment Saturday.