Grayson has seen his odds cut – to 7/4 favourite in the last 24-hours or so - to take charge at the Suit Direct Stadium.
Paul Hartley, having been linked in the Scottish press, has also seen his odds cut but it is Grayson that is now the leading contender to take charge at Pools.
Pete Wild has also once again been strongly linked since Lee was sacked but Barrow are leading the chase to secure Wild’s signature, he is currently involved in the National League play-offs with FC Halifax Town.
Lee was sacked prior to the final game of the League Two campaign.
A club statement outlined clearly the reasons behind Lee’s sacking: “Since losing to Rotherham United on 9th March, the team has won only one of 11 games, picking up just seven points and scoring eight goals.
“Additionally, previously strong home form has not been maintained with no home win since 15th February, resulting in just three points and only three goals in seven games during this period.”