Hiddink, 69, managed Chelsea after Luiz Felipe Scolari was dismissed in 2009. Hiddink led the side to the 2009 FA Cup.
Mourinho left the club by mutual consent after a disastrous four months in the English Premier League. His players have lost nine of their 16 games of the 2015/16 campaign. Last season they were crowned champions with three matches to spare.
Chelsea, who are 16th and one point above the relegation zone, face Sunderland on Saturday at Stamford Brige.
Mourinho departed with the club citing that relations with several players were bad. However even Hiddink's appointment might not guarantee any improvements. His reputation has suffered since his last stint in west London.
He has had poor pells as manager of Turkey, the Russian side Anzhi Makhachkala and the Netherlands.
He stood down as coach of the national side in June, with their Euro 2016 qualifying hopes in disarray.
The Dutch failed to reach next summer's finals, finishing fourth in their group, behind Czech Republic, Iceland and Turkey.
On Friday, Chelsea captain John Terry described Mourinho's exit after 30 months in charge as a "sad, sad day".
Terry, 35, was appointed skipper by Mourinho when he first went to Chelsea in 2004. The former England international was the lynchpin of his defence during Mourinho's three Premier League titles with the club.
"Going to miss you boss," Terry wrote on Instagram. "The very best I have ever worked with, unbelievable memories together. Thank you doesn't seem enough."
Meanwhile even with the possible sop of Hiddink as interim manager, there was discontent from the fans.
"It was fundamentally obvious that there was something wrong in that dressing room," said Mark Worrall, a writer on the Chelsea fans magazine CFCUK. "But there's a real undercurrent of anger towards the board for pulling the trigger in the way that they've done.
"Everybody feels marooned because Jose was one of the fans and now that he's gone, people are looking at each other and asking what next? Who can we identify with now? Whoever comes in as an interim manager, what do they hope to achieve?"
With retaining the title a diminished reality, a finish in the top four - and qualification for next season's Uefa Champions League unlikely - the club executives will target progress in this year's competition as well as a good showing in the FA Cup.