The 27-year old Romanian centre-back looks set to depart The Hawthorns after joining from Dianmo Bucharest in January 2010.
His agent, Ivan Reggiani, confirmed that Tamas would be on his way to the Roman club to join fellow Romanian Stefan Radu.
"We are in negotiations and Lazio like the lad very much," Reggiani told lalaziosiamonoi.
"He is fascinated by the chance to play alongside his fellow countryman, Stefan Radu.
"The Biancocelesti remain our priority and we've been in talks with them for over a month.
"We are at an advanced stage and Tamas is very likely to wear the Lazio shirt next season. The only doubts are around his behaviour.
"President Claudio Lotito and director Igli Tare are considering this aspect, but I can assure them Tamas is an exemplary professional.
"He's always the first to arrive at training and the last to leave."