Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Tamas has proved himself a worthy understudy to the first choice centre-back pairing of Jonas Olsson and Gareth McAuley.
His current contract runs out this summer although Albion could take up a 12-month option.
Tamas, who joined Albion three years ago from Auxerre after an initial loan spell, said: "I would like to stay here until the end of my career.
"I hope to play football for another decade, maybe up until I am 38 or 40.
"Staying at the same club for several years has helped my career become more stable.
"I have even talked to people at the club about extending my contract.?
Tamas, 29, admits he is settled and content with life in the midlands.
He said: "My life has changed so much for the better. I enjoy my quiet life in England.
"To me, the family means a lot. I don't bother anyone. I go to work smiling and then I smile when I get back."
Meanwhile, Baggies striker Peter Odemwingie is set to return to training on Wednesday after his latest Twitter attack against the club.
The Baggies have confirmed they will deal internally with his outburst.
The 31-year-old said he was unhappy at being a substitute in recent games and when one fan tweeted that he should be sacked, Odemwingie replied that is my wish".
An Albion spokesman said: "The club are aware of what Peter has said and we will deal with it internally."
West Brom also confirmed that social networking activity is governed by the club's disciplinary code of conduct.