There are doubts surrounding Roy Hodgson's future at Crystal Palace.
The 73-year-old's contract at Palace runs out in the summer and there has been reports that he could retire at the end of the season.
Hodgson refused to discuss his future at the club when asked about it on Monday.
"As I have said all along, I want to finish this season well and we don't in any way want to do anything that will affect our chances of playing and doing well in the final games," he said, per Sky Sports.
"Let's get those games done and then there is plenty of time to give answers to any particular questions I would get, but I am not prepared to do it at this moment in time because there are more important things on the horizon for me."
With uncertainty about Hodgson's future, Palace have started at looking for his potential replacements.
Many names have been touted but one high-profile manager is now reportedly the frontrunner to replace Hodgson.
What is the latest Crystal Palace manager news?
Sean Dyche and Eddie Howe have both been linked with the job but it is believed Lampard has moved ahead of them both.
What does Lampard think about potentially managing Palace?
The report says it is unclear whether Lampard will immediately accept the role or wait to access his options.
It does add, though, that Lampard will no doubt want assurances that he would be given the opportunity to try and progress Palace up the Premier League table.
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Palace currently have 11 players whose contract runs out in the summer.
If Steve Parish wants Lampard to be the new Palace manager, it is up to him as chairman to give Lampard the assurances that he desires.