Bullard has been out of action since January when he picked up a knee injury in the game against West Ham in his debut game.
Tigers’ manager Phil Brown will be taking a look at the 30 year old in a private game with York City on Tuesday afternoon.
"Whether or not Jimmy will be able to start against Fulham will depend entirely on how he does against York and how he trains for the rest of the week," Brown told the Hull Daily Mail.
"His attitude has been absolutely first class but we'll only play Jimmy at the right time.
"It was 45 minutes under his belt last week, albeit reserves, and hopefully there will be another 60, 65 or 70 minutes against York.
"If he comes through unscathed again, fingers crossed he could play some part in the Fulham game, but I'll be keeping my cards close to my chest with regards to how much."