Begovic briefly worked under Mourinho at Chelsea early on in the season.
Begovic was signed by Chelsea during Mourinho's time there last summer, but the two only worked together for a few months after a disastrous start to the Blues' title defence saw them hovering just above the relegation zone, with Mourinho sacked in December.
Now it would be very surprising if Mourinho was not leading Manchester United at the start of next season after they announced that Louis van Gaal would be leaving the club yesterday, just two days after they lifted the FA Cup after a disappointing league campaign which saw them finish in fifth.
Begovic told Sky Sports: "Man United will be a team to be reckoned with next year, they will look to get into the Champions League once again and aiming for the top, and even to win the league.
"Generally having Jose Mourinho in the Premier League is a great thing, he's a great character, he's one of the best managers in the world - it's great to have him back in football.
"I'm obviously thankful to him for bringing me to Chelsea and the experience of working with him for a few months was priceless. His knowledge of the game is second to none, is tactical approach is fantastic."
Given Mourinho's record both at home and abroad - despite the last few months that brought his Chelsea tenure to an end - many will tip him to add to his lengthy honours list at Old Trafford.
Yet when his appointment is confirmed, many will have an eager eye on just how much transfer activity will take place at the club.