The Tigers are in the hunt for a new boss to replace Shota Arveladze.
Grant, 67, last managed in England back in 2011 and his last job came in 2018 in India with NorthEast United.
According to a report by Hull Live, he has declared an ‘interest’ in the vacancy at the MKM Stadium.
Other names in the frame for the Championship side are Carlos Carvalhal and Pedro Martins.
Chelsea and West Ham days
Chelsea turned to Grant in September 2007 and he went on to spend eight months at the helm at Stamford Bridge.
He guided the London club to the Champions League final during his time there but they were defeated by Manchester United on penalties.
The Israeli manager then had a spell at Portsmouth before West Ham came calling in 2010. However, his stint with the Hammers lasted just a single campaign and he was dismissed after 15 wins out of 47 matches.
Grant has since had spells at Partizan, Ghana and NorthEast United and is now weighing up his next move in the game.
The Hull job has become available and they will be a good project for somebody under their ambitious owner Acun Ilicali. They have made a poor start to this campaign though and are sat in 20th place.