Mills has always insisted Johnson is his number one target to replace Mark Stallard, but also said he won't wait for ever.
"We have a certain budget here and I don't believe we are in a position to bring in two strikers so I want to make sure we get the best we can.
"At the moment I believe that is Tommy but we can't wait too long.
"I am not setting any specific deadlines but if we get to Thursday and it still hasn't happened then we will have to consider our options."
And Mills said he has other targets if necessary.
"I do have other targets in mind and we will have to start looking at those at the end of the week," he added.
"But I am still very positive about the situation. I still believe we can get him.
"We let Mark Stallard go and I still believe it was the right decision to make as it has given us some money to work with and I am happy with what we have done so far.
"I am pleased with the way the new signings have settled.
"I believe that, in the space of two weeks, the squad has got a lot stronger but hopefully we can make it stronger again."