The 29-year-old Romania international is in the final year of his contract but Albion have the option of a 12-month extension in their favour.
The Baggies have already opened contract talks with centre-back Gareth McAuley and striker Shane Long, and Tamas indicated last week that he wants to remain at the Hawthorns for the rest of his career.
However, West Brom head coach Steve Clarke said: "Gabby is one of a number of players where we will probably look at the situation at the end of the season.
"For now, there are no talks with Gabby. We have talks ongoing with one or two players just now - but you can't talk to everyone at the same time.
"Gabby will be addressed at the end of the season."
Pressed on the futures of McAuley and Long, Clarke said: "We are still talking. Richard Garlick [Albion's technical director] went to Ireland to speak to one of Shane's advisors, but I don't know how it went because I haven't spoken to him."