Mourinho, who said he had gone from being the 'Special One' to the 'Happy One' when he returned in June for a second spell as coach at his spiritual Stamford Bridge home following spells at Inter Milan and Real Madrid, has made no secret of his desire to sign the England striker.
Rooney also seems keen to end his nine-year spell at Manchester United for a move to Chelsea but can United afford to allow their prize asset to reinforce the title claims of one of their leading Premier League rivals?
Mourinho has already had two sizeable bids for Rooney rejected and former United and England captain Bryan Robson believes he will need to wave a huge financial carrot in front of the Old Trafford hierarchy in order to seal the deal.
"The thing that makes me laugh is I've been told it (the latest offer) is 25 million pounds to 30 million pounds ($46.38 million)," Robson told Talksport radio.
"For Wayne Rooney? A 27-year-old who is probably in the top six strikers in the world? What are United going to have to pay to replace him? I'm amazed at that - it's an insult to Wayne Rooney."
Insult or not, Mourinho is prepared to play a waiting game, content in the knowledge he can already call upon three good strikers in Fernando Torres, Romelu Lukaku and Demba Ba.
Torres has often flattered to deceive since joining Chelsea for a record fee of 50 million pounds from Liverpool two and a half years ago although he showed signs of improvement last season.
The Spain striker bagged 23 goals in all competitions including a dazzling run from the halfway line to score the equaliser in the 2-1 Europa League final victory over Benfica in Amsterdam in May.
Mourinho believes Torres, who is at his best when balls are played beyond the opposition defence for him to use his pace, is capable of flourishing if his team mates utilise his strengths.
"When we see Torres with his back to goal surrounded by two or three opponents we know he is not going to produce a piece of magic," said the coach who led Chelsea to back-to-back Premier League titles in 2005 and 2006.
"But this is Torres. We want the team not to learn how to play with him but to improve how to play with him," said Mourinho who is adored by the Chelsea fans and will get a special welcome at his first game back at home to Hull City on Sunday.
"It is impossible to re-model his game but we want to adapt the team and teach the team how to use his best qualities. He is what he is and he is very good with the qualities he has got so we need to learn and support his game."
Chelsea, who finished third in the Premier League under interim coach Rafael Benitez last season, have been boosted by the signing of Germany forward Andre Schuerrle from Bayer Leverkusen.
Mourinho also swooped for young Dutch international midfielder Marco van Ginkel in the close season while midfielder Michael Essien, winger Kevin de Bruyne and utility player Nathaniel Chalobah have returned after loan spells elsewhere.
It is the return of the charismatic Portuguese coach, however, that has attracted so much attention to 2012 European champions Chelsea.
"The Premier League requires a Jose Mourinho character more than ever," said former United and England defender Gary Neville. "He is the biggest signing of the summer for English football.
"You can't ignore him, the way he challenges people, works the media or celebrates on the touchline like a fan. Whoever you support you should be delighted to have Jose Mourinho back for the new season." ($1 = 0.6468 British pounds)