Andre Villas-Boas was sacked on Monday morning after a heavy defeat to Liverpool, having only taken charge at White Hart Lane in the summer of 2012.
Hoddle - a Tottenham great as a player - managed the club between 2001 and 2003 but has been out of management since he left Wolves in 2006.
But Lineker feels that now is the time for him to make a return.
England's record goalscorer wrote on Twitter: "AVB has been sacked by Spurs. Would love to see Glenn Hoddle given another chance at this level. Has a brilliant football mind."
Villas-Boas watched on as Spurs were beaten 5-0 by Liverpool, just three weeks after a six-goal thrashing at Manchester City.
That loss at the Etihad Stadium prompted former Spurs chairman Lord Sugar to call for the Portuguese to be sacked and Sir Alex Ferguson to be appointed.
Sugar had scaled down his expectations on Monday, though, tweeting: "Spurs need to put Les Ferdinand and Tim Sherwood in charge for a while".