The seventh-placed Saints have already seen striker Michael O'Halloran come in from Bolton this transfer window, while David Robertson and Sanel Jahic have been released and Gwion Edwards has returned to Swansea following a loan spell.
While Wright wants to do more business this January - with a striker a priority - he admits there must be more departures first.
He told the Daily Record: "We need to get people out before we can bring people in and that hasn't changed.
"We are looking for a striker and I'll be meeting the chairman to put a few options to him."
Wright hopes to keep top-scorer Stevie May at the club but if he was to go, then the Saints boss wants a deal done quickly so he has time to bolster.
He added: "Hopefully we can keep Stevie. If he goes early in the month, at least it gives you time while our resources would improve as he'll go for a sum of money."