Former Bhoys midfielder Neil Lennon has been in interim charge since Rodgers left to manage Leicester last month, but Collins reckons the Ladbrokes Premiership leaders are keen on hiring Martinez.
The current Belgium national team boss, who took the Red Devils to the semi-finals of the 2018 World Cup in Russia, has been linked with the Celtic job before, and spoke about it last year.
Addressing claims he had held talks with the Hoops following the departure of Gordon Strachan in 2009, the former Motherwell midfielder said: “I had conversations and I was always very impressed with the need to bring silverware.
“The opportunity of having conversations with Celtic is something that fills you with pride.
“It is a club with great tradition and a club that demands qualification in the Champions League. You can appreciate the status of the football club.”
Collins was appearing on RockSport Radio when he claimed that Martinez could be on the Celtic hierarchy’s radar - and that he could bring Shaun Maloney back to the club as his assistant.
He said: “I genuinely believe Martinez and Shaun Maloney [will be hired]. I don’t think the deal is done, I think they’re still negotiating on that deal.
“If it’s Neil Lennon [who gets the job] - fine, then Neil Lennon can maybe go and get their 10-in-a-row, but the character of whoever comes in has got to be a hero.
“If it’s not Lenny, I think it’s Martinez, along with Shaun Maloney. He’s the type of manager that Celtic want, he plays good football.”