Ashley also has a stake in the Rangers International Football Club plc and Sports Direct already has an agreement as Rangers'' merchandising partner.
Charles Green, the Rangers chief executive, hopes to have the naming rights in place before the start of next season.
Green told STV: "We have now decided that Sports Direct will be the partner [for stadium naming].
"We had representatives from Sports Direct up for a fans'' forum a couple of weeks ago.
"We also had Derek Llambias of Newcastle United sharing his experience of how that helped his club.
"We are now into the stage where we are doing some layouts, some pictorials of how it might look and we''ll stick those on the website shortly so the fans can see what''s being proposed.
"We have had good engagement from the fans on this.
"I think it was always an issue for fans but I think the fans accept now that this is something that we have to do.
"Almost all of the big stadia have been named now."
There was concern on Wearside this week when the Mackem board said they were open to offers to re-name the Stadium of Light - which is a name pinched off Benfica.
I don''t believe for a second many would be opposed to a change of name - because they have had the piss taken out of