Mourinho has been out of work since being sacked by Chelsea in December, but has been heavily linked with Beckham's former club Manchester United, who continue to struggle under Louis van Gaal.
And the ex-England captain says he would be thrilled to see the Portuguese return to English football.
READ MORE | FA Cup win a stay of execution for Van Gaal
"I hope Mourinho comes back to the Premier League very soon," Beckham told talkSPORT.
"We need characters like that in the game."
Inter official Bedy Moratti further fuelled speculation that Mourinho is on his way to Old Trafford last week by claiming the Portuguese coach is "going to Manchester" after enjoying lunch with the ex-Nerazzuri boss.
"He is happy now. He is going to Manchester, so he is doing great," she told reporters after the meeting.