Magilton is keen to bring Wright back to Portman Road, but is waiting on a response from the Hammers.
"We are not prepared to wait too much longer," Magilton told the East Anglian Daily Times. "We would like to get something tied up by the end of the week at the latest.
"I will give it a few more days and see how the land lies and I hope a deal can be concluded, if not we will look elsewhere.
"We have to have other irons in the fire and we are constantly on the lookout for the right sort. If it is not Richard it will be someone else.
"There is another goalkeeper we are in talks with.
"Richard Wright coming back ticks all our boxes. We are a club he knows well and I would like to take him back, but it is not ticking West Ham's boxes at the moment, because if they lose a keeper they need a replacement and until they get a replacement, Richard is not going anywhere.
"But if they can get someone in and it frees up Richard, then we are in a position to take him."