While the club are increasing the pressure on Real Madrid target Arjen Robben to make up his mind over his future, the Blues are willing to play a waiting game with Lampard.
The England midfielder, like Robben, also has two years left on his contract and has refused the club's offer.
However, his agent Steve Kutner, insists the stalemate will not affect his form.
Kutner said: "If it goes all the way to the last day of Frank's current contract, one thing's certain, Frank will not waver in his commitment to Chelsea."
Blues boss Jose Mourinho wants Lampard to pledge his future to the club but the midfielder is still not entirely happy with the terms of the contract offered to him by the club.
It has increased speculation in Europe that Barcelona will test Chelsea's resolve yet further by making another attempt to land him.
However, Chelsea's veteran midfielder Claude Makelele is ready to sign for a further year after looking almost certain to leave during the summer.
The France international found it hard to hold down a first team place last season after a disagreement with Mourinho over the player's decision to continue turning out for his national side.
But Makelele's experience will be vital for Chelsea as they attempt to wrestle the title back from Manchester United and the midfielder appears to be on the brink of staying at Stamford Bridge for a little longer.
Chelsea's unbeaten pre-season run came to an end against Rangers on Saturday and they now travel to Denmark to play Brondby tomorrow night.
But winger Shaun Wright-Phillips insists the defeat at Ibrox has already been forgotten.
Wright-Phillips, who replaced Joe Cole at half-time in Saturday's 2-0 defeat, is keen to look forward to the challenge in Copenhagen.
He said: "I just want to get it out of my head to be honest. That's it now, we're on to the next game and we just have to prepare and play well.
"I think every game we play is good preparation. We need to use it for gelling and fitness, and getting results to get our confidence up."
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