Town boss Russell Slade previously admitted Sills was a player he was aware of but no offer had been made.
Now Sills claims he was made a solid offer by Town but is waiting to see what the Shots have in return.
"Grimsby were interested in me but they wanted me to go up and sign on the dotted line last week. I didn't want to do that and felt I should hear from Aldershot first," he told the Aldershot News and Mail.
With Slade set to sign a striker on Monday, Sills will no doubt be the favourite.