Warnock told sufc.co.uk "We have tabled a bid of around £500,000 as we need a striker of his caliber. He has good movement, an eye for a goal, and is very athletic. He's from Sheffield, and we think he would do an excellent job for the Blades.
"Other clubs are interested, and it remains to be seen whether Liverpool would be prepared to sell Neil to anyone at this time, or whether they would prefer to wait until the January transfer window. We'll have to wait and see.
"I've made bids for three strikers, all different types of player, but all of real quality. It's a question of seeing which of them becomes available. If one does, I'd have to take a chance on him without knowing how the other two situations might unfold."
The Liverpool striker, who was on loan to West Ham last season looks to have had his moved blocked after it emerged that Milan Baros left the field early in an Czech Republic International last night. This leaves the Reds short on attackers and could see Mellor join in January when all the players are back fit.