Mourinho has come under pressure this season due to Chelsea’s poor results.
Former Tottenham man Crooks believes that if Chelsea do sack Mourinho, then they should look at Koeman as a replacement.
“So why are the press fuelling the speculation around Brendan Rodgers, Roberto Di Matteo or Guus Hiddink taking over at Chelsea?
“Blues owner Roman Abramovich would be stark raving mad to part company with Jose Mourinho, but if he did why wouldn't you go for Koeman?”
Koeman has been in charge of Southampton since the summer of 2014, and he has done a truly remarkable job at St. Mary’s Stadium.
Under the Dutchman, the Saints finished seventh in the Premier League last season.
Southampton are seventh in the standings at the moment and are in the running for top-four finish in the league this campaign.