Wright is out of contract at the end of the season and has yet to agree on the terms of a new deal at Pittodria.
Steven Gerrard’s side could offer the 23-year-old a pre-contract now, but Sky Sports News understands they are looking to secure a deal in this window.
Wright, who has scored two goals in 17 appearances so far this season, recently returned from a six-week layoff after suffering from a double hernia.
It started on Sunday in Rangers’ 2-1 win over Aberdeen at Pittodrie.
Aberdeen boss Derek McInnes recently revealed that Wright has indicated he wants to explore options away from Granite City.
McInnes told the Evening express: “It looks like Scott is looking to try something different, maybe looking south unfortunately. From our perspective, we really want Scott to stay, but he just wants to keep his options open up to the minute. ”
“We did everything we could to try to get Scott to stay. But we are now four months away and we are no further ahead. We have not been able to reach an agreement. Scott and his agent have indicated that they wish to look into the matter. options and are not able to commit. ”