But Redknapp perceived a future for the midfielder in more august surrounds and brought him to West Ham for £30,000.
What was once a transfer fee is less than the weekly wage Bullard is now believed to be demanding from Fulham, and as he prepares to face his former mentor at White Hart Lane on Boxing Day, there are suspicions that if the impasse is not broken a reunion at Tottenham could be imminent.
Redknapp, in danger of losing Didier Zokora to Real Madrid next month, could use a midfielder of Bullard's ingenuity to enhance his attacking options, but denied an approach to Fulham had been made.
Bullard has been instrumental in Fulham's surge to eighth in the Premier League, scoring in the win over Middlesbrough last Saturday, and is understood to have asked for a pay increase to £50,000 a week.
It marks quite a spectacular shift in perspective for a player who could not even break into the West Ham first team, but Redknapp said: "I've not made an inquiry about Jimmy and nor has the club. He's still contracted to his club. I do know him and he has done fantastically well. He is a great lad, character and personality. He has turned out to be a top player.
"I took him from Gravesend because I thought he had something. Otherwise we wouldn't have got him. After I left they let him go. He's developed since then and that is full credit to him."
Much of Bullard's development can be traced to the tutelage of his manager at Peterborough, Barry Fry, who shared Redknapp's uncomplicated motivation techniques, although he has also flourished under the more cerebral Roy Hodgson, reviving his Fulham career and returning to the England reckoning after a long-term knee injury.
Redknapp purports to have earmarked up to four players to enhance his squad in January and while Bullard would satisfy his desire for more creativity in the centre, the 29-year-old's chances of joining Tottenham are potentially limited by the blossoming of Luka Modric.
The Croatia playmaker, anonymous under Ramos, has been transformed by Redknapp's deployment of him in a more mobile station behind lone striker Darren Bent, and was arguably the best player on the pitch in last Sunday's defeat to Newcastle.
"He was terrific against Newcastle," acknowledged Redknapp, who has been in regular contact with Croatia manager and one-time West Ham protege Slaven Bilic about how best to harness Modric's talents.
"He's an outstanding footballer. Slaven thinks he's world-class and I think he has the ability to be, too. He's the type of lad you look to build your team around – if you can get him on the ball things can happen. It's about getting good people around him with movement to capitalise on what he can do.
"He's only just starting to play in the position he wants – before that he was played wide. His position really is behind a striker if you can play that system with him. He's got to be in a position to affect the game and since I've been here we've got him there; that is probably why his form has been good."
Tottenham, having definitively shelved their interest in Andrei Arshavin of Zenit St Petersburg, could shift their attention to the less expensive Bullard as the quest to find complements for Modric's skill intensifies.