Mourinho is expected to be confirmed as The Premiership's big-spenders' new manager in the coming days and will replace Claudio Ranieri at the helm.
He has been tipped to raid Porto for several of the players who helped the club to win the UEFA Champions League, with playmaker Deco believed to be the prime target.
But midfield anchor man Costinha has confirmed he wants to link up with Mourinho in London and is hoping a deal can be arranged.
Costinha, who has two years remaining on his contract, is a key figure for Porto and he is likely to cost in the region of £7 million.
"Do I want to follow Mourinho? Of course, why not?" commented Costinha in the Sunday Mirror.
"I have to be careful because I still have two years left on my contract at Porto but if I could choose of course I would like to go with him because I know if I go then I will have more success.
"My agent is taking care of it and I know there will be developments over the next few days."
Costinha also hailed the methods of Mourinho, whose success in steering Porto to European glory elevated him to the position of the most sought-after coach on the continent.
"He is probably the best trainer I've ever had," added the Portuguese international. "He knows how to prepare the players and how to speak with them.
"He thinks about football 24 hours a day. He is always wondering where he can improve his team, where he can make better use of a player.
"He is fair with everybody. He is not one way with the star of the team and different with a youth player.
"There are no superstars for him. The most important thing is the team."
