The former Chelsea manager has been strongly linked with taking over at United, and following Ferguson's son Darren's comments last week that the Scot will retire next season, speculation has increased.
When asked if he would consider the role, Mourinho told ESPN: "Who can say no? Nobody could say 'no'.
Since the end of the 2001/02 season, Ferguson, has refused to speculate as to when he will retire, and in spite of Darren's revelations, Mourinho is confident the 67-year-old will be at United's helm for some years to come.
"First of all I don't believe in 2010 he is leaving - I don't believe," he said. "I think year after year he is the same, he's exactly the same person; healthy, happy. so I don't see a reason for him to quit.
"And in a very fair way, I hope he still goes, I hope he still goes on, because he's good."
The two coaches' relationship over the years has had its ups and down - most recently with United knocking Inter out of this season's Champions League.
But despite the club rivalry, Mourinho sees a host of similarities between himself and Ferguson.
He said: "I think we have some points in common; huge ambition, desire, big pleasure in football. The fact he's almost 70 and he keeps saying he still enjoys his work is exactly the feeling I have at 45. I look to my 60s, and for sure I will have the same kind of mentality I have today.
"Close relation with the players, and with our club fans, so yes I think we have some points in common, and also after matches, we have in common, the fact that we know how to lose and we know how to win."