Ghana coach Avram has given a hint at a possible exit when his contract expires in 2017.
The 60-year-old could be returning to England where he has had most of his coaching career.
Grant has already been reported to be in talks with some English Club over the possibility of moving after the Cup of Nations in Gabon.
The former Chelsea boss in an interview with Israeli radio station 102FM hinted he could leave his post as Black Stars coach in the next few months.
"The competitiveness and creativity in training every day of the week is different. There is no doubt that I miss it," Grant told Israeli radio station 102FM.
"My contract ends after the African Cup of Nations Championships in Gabon early next year.
"Next year, at the end of my contract, it is possible I will coach a team in England."
The Israeli tactician who has a running contract with the Ghana Football Association has managed the likes of West Ham united and Portsmouth.
Grant, having missed out narrowly on the Cup of Nations trophy in 2015 will be hoping to make history by becoming the first expatiate coach to win the Cp of Nations with the Black Stars.
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