Mourinho has faced scrutiny following a run of four games without a win and off-field controversies including a row with midfielder Paul Pogba.
Giggs, an Old Trafford legend after 25 years at the club as a player and coach, has been tipped as a future United manager.
“I believe he [Mourinho] should keep his job,” said Giggs.
“They’re going through a tough time at the moment, but change now then you’re in the same position in a year, two years, quite possibly.
Giggs, speaking at the squad announcement for Wales’ games against Spain and the Republic of Ireland, added: “I think the problem of late has been forward planning. Just take stock, they’re going through a tough time but, no, my stance hasn’t changed.”