The former Manchester United and Chelsea boss has been linked with a move to the French side, following the news that current head coach Bruno Genesio will leave the club at the end of the season.
Speaking in a press conference on Saturday, Genesio said: “For some time, I've been facing - we've been facing - a negative climate, which can be a drag on the players and the club.
“I had a very long conversation this morning with my president, in order to tell him that I will not continue next year.”
That led to speculation on that Mourinho could be in line to become the next head coach at Lyon.
However, Campos, who worked with the Portuguese manager during this time at Real Madrid, has claimed he finds it unlikely that Mourinho will begin the 2019-20 season at Lyon.
“He has won everywhere,” said Campos, when speaking to Telefoot. “Lyon is a great club, but I think that he is looking for an even bigger project. And, he is expensive."
Should Mourinho not take the Ligue 1 post, Laurent Blanc has also been linked with the soon-to-be-vacant position.
Luis Campos sur une éventuelle arrivée de José Mourinho à Lyon :" Il a gagné partout. Lyon c’est un grand club. Mais je pense qu’il vise un projet encore plus grand et il coûte cher". #Téléfoot pic.twitter.com/6xifMnhN0A— Téléfoot (@telefoot_TF1) 14 April 2019
Mourinho has been out of a job since leaving Manchester United in December, but recently claimed he has turned down ‘three or four offers’, yet stated he would like to be back in football management by June.
As for Lyon, they face a battle to secure their Champions League place for next season. Les Gones are currently third in the Ligue 1 table having picked up 56 points from 32 games this season and, crucially, are five points ahead of their nearest challengers, Marseille.
They did, however, suffer a disappointing defeat to 15th-place Nantes on Friday night, going down 2-1 thanks to strikes from Kalifa Coulibaly and Anthony Limbombe.
Next up for Lyon, they host Angers on Friday night.