The Spaniard has been under fire since his controversial appointment at Stamford Bridge last month, with his unpopularity amongst fans in large part down to comments he made about the west Londoners and their fans whilst Liverpool boss.
Benitez has hardly done much to inspire faith with two draws and a defeat in his opening three Barclays Premier League games - scoring just one goal in that time - to slip 10 points behind leaders Manchester United.
There are already reports that owner Roman Abramovich is looking to replace Benitez but Grant shot down rumours linking him with a return to the club he guided to the Champions League final in 2008 and added the former Valencia boss needs to be fully supported by the Blues.
"Nobody from Chelsea has offered me this job," the Israeli told BBC Radio 5 Live.
"I heard a rumour but I think this is not what's important.
"What's important is Chelsea have a manager and the club need to support him and not look for any other things."
When asked if he would consider working alongside Benitez, Grant responded: "I don't think it's the right idea for the moment.
"I don't like to speak about myself now because I have other things to do at this stage.
"I think Benitez is a very experienced coach and manager and I don't think a few weeks after they give him the job he will leave and I don't think it will be right.
"He needs to use all experience to take the club in a different direction and they need to do everything to support him and not to look around."
Benitez did at least claim his first victory with the Blues on Wednesday although a 6-1 Champions League win over FC Nordsjaelland was not enough to seal a passage to the knockout stages following Juventus' 1-0 win at Shakhtar Donetsk.
Chelsea instead became the first holders of the Champions League crown to drop out of the tournament at the group stage.
Grant, who was last in charge of Partizan Belgrade, believes Chelsea need to carry on winning in order to convince the club's supporters Benitez is the man for the job.
"Any winning is good and what Rafa needs is a good win and good football really to convince the supporters that they need to support him," he added.
"But I think more than this the club needs to support him then it will be easy for him because it's not easy times for Chelsea, first time out of the Champions League next stage and the gap between them and the first place in the league, I think he needs it and they need it."