no, he can not make offer if you do not have money for that. but for example a player worth 1.5M, 1.3M at auction is, you have 1.3M, just do offer if after the auction to continue the heats the price will increase player, you're not going to have enough money but you can continue token to bet on the player.

concluding, what matters is if you have money to make the first offer to the player if the player then raise the price, you can keep trying to hire you but you stay with a negative balance.