Chelsea are now searching for a new manager to replace Mauricio Pochettino after announcing on Tuesday that the Argentine has left Stamford Bridge by mutual consent.
Amorim, meanwhile, has guided Sporting to victory in the Portuguese Primeira Liga this season and also has the chance to make it a domestic double if his side beat Porto in the Taca de Portugal final this Sunday.
The 39-year-old is understood to be highly regarded by Chelsea’s hierarchy, while last month, he held talks with West Ham, who are seeking a replacement for David Moyes.
However, during Sporting’s Portuguese Primeira Liga title celebrations in Lisbon on Monday, the club’s president, Frederico Varandas, made it clear that Amorim was not going anywhere this summer.
‘Today, we have one of the best coaches in the world,’ Varandas said.
‘We have him today, we had him four years ago and we have him next year.
‘It is not because of the financial aspect or the lack of interest from other clubs that he remains here, year after year. He stays here because Sporting is a club that gives you protection, stability, conditions to be successful and above all to be happy.’
Speaking earlier this month, Amorim also gave no indication that he is seeking to leave Sporting this summer.
‘We don’t control the future, but I’m very focused on Sporting and on work,’ Amorim said.
‘The mistakes I made in the past, I certainly won’t make in the future, my focus is just on Sporting and we are planning the next season in as much detail as possible.’
Amorim had previously issued an apology four weeks ago for travelling to London to hold talks with West Ham.
‘My trip was a mistake. The timing was completely off, it didn’t seem right to me at the time,’ Amorim said.
‘It was inappropriate, even more so when I am so demanding with my players, I am always the first to say that each one’s individual problems cannot be overcome by the team and, therefore, it was my fault.
‘I have to accept it and live with it. Thinking coldly afterwards, it is very clear.’