The ex-Newcastle striker has been released by Portsmouth and the Tigers are said to ready to offer him a one-year contract.
Cole joined Newcastle in 1993 and made 84 appearances - scoring an amazing 68 goals.
Signed from Bristol City and took the place by storm with his powerful running, superb finishing, and uncanny partnership with Peter Beardsley.
Left under a cloud when he was sold to Manchester United and mocked Kevin Keegan for selling him. Later played for Blackburn and Fulham.
Although Cole's deal seems genuine, Hull have been at loggerheads with their fans in recent days after they said they were ready to sign Brazilian world cup star ... and ex-Smoggy ... Juninho.
Hull were accused of using Juninho as a publicity stunt after a move to take the former Middlesbrough star to the club lay in ruins.
The 2002 World Cup winner flew into England to hold talks with Hull chairman Paul Duffen and manager Phil Brown last week, and terms were agreed in principle on a one-year deal to make Juninho the club's highest-paid player.
But Duffen has now pulled the plug on the move and hinted Juninho's arrival could have disrupted the harmony within Brown's squad.
That has provoked an furious response from Juninho's agent, Jonathan Hassall, who feels Duffen may have courted the Brazilian's services in order to publicise a club which he bought last month from Adam Pearson.
Hassall said: "We just feel that he's a new guy who has come into football and used Juninho to publicise Hull but then backtracked on what he's said.
"He wanted a World Cup star and the publicity it has created has got Hull on radio, television and in the newspapers.
"The interest he's created has been frightening but I fear he has just been used as a marketing tool.
"We are dealing with a player who's played 50 times for the best footballing nation in the world.
"But I spoke to Phil Brown last night and he said that his chairman (Duffen) has gone on radio saying that the deal was off - although he's not had the decency to get in touch with me.
"Looking at it, it looks like he just kept us dangling, milked the publicity and then pulled the plug."