"What is going on with the FA? When are they going to decide or even approach some form of England manager or let Stuart Pearce know he's got [the job] for the Euros? Somebody has to prepare," Lineker told BBC Radio Five Live.
"The only reason I can think of - which I'm sure is the reason - is that they don't want to upset any club's applecart."
Spurs boss Harry Redknapp has been widely tipped for the England job, and Lineker believes that the FA no longer has anything to lose by making an approach.
"If they were going to go for Harry Redknapp, which we all presume they will, they don't want to upset the end of Spurs' season - but it seems they have already done that now so they might as well get on with it," he added.
"They may think everything is in place and there are no [England] games until the end of the season, the training camp is all sorted, but the new man needs to start thinking and planning his team.
"He needs to start thinking and planning about how other teams play and do his homework on them and things like that, now they're running out of time. If they were going to go with anybody, they should have done it by now."
Lineker earned 80 caps for England, scoring 48 goals.