By ESPNSTAR.com staff
British tabloid The Sun claims the 34-year-old is "wanted" by Chinese Super League rivals Shanghai Shenhua and Beijing Guoan.
Lampard's contract expires at the end of the current European football season but he can speak to clubs about a summer free transfer as early as January.
The Sun reports that Shanghai Shenhua, who already have Lampard's former Chelsea team-mate Didier Drogba on their books, and Beijing Guoan are both "ready to offer that mega-bucks £1 million a month jackpot" to Lampard.
It also speculated that Lampard "appears on his way out" at Stamford Bridge after 11 years because Chelsea have a policy of offering only one-year extensions to players aged over 30.
However, current Blues boss Roberto Di Matteo recently told reporters at a press conference that the England international remains part of his plans even if Lampard no longer commands first XI place in every game.
"His future is very strong at this club. He's a very important player for us," Di Matteo said earlier in the month.
"I've had conversations with him, yeah, which I do on a regular basis with the players. I like to exchange opinions.
"He's very supportive of the team when he's not in the team. When he's in the team, he's a great performer as well.
"From that point of view, we're fortunate to have a very strong squad with international players, so that's going forward with a busy schedule, it's important we use these players."
Di Matteo hinted that Lampard could prolong his career in the top flight of English football by adapting his game from a box-to-box goalscoring midfielder to an anchorman.
"He's been playing that role, but I don't think I've ever taken those other things away from him. Those are his strengths, but you sometimes need discipline in that role. It's important for the balance of the team," he said.
"But he's played there magnificently at the beginning of this season and last season as well."