Taylor, 36, was released after making an emotional final appearance for the Baggies against Newcastle at the Hawthorns. He had spent 9 seasons at West Brom in two spells.
It is thought that two clubs have emerged as major possibilities to sign him, Cheltenham Town and Walsall. Taylor has said that he wants to play at the highest level he can though, so Cheltenham's relegation will not help their chances of signing him.
The Robins do have one advantage though, and that is that Taylor gets on very well with Robins manager Bobby Gould.
Gould signed Taylor from Bristol City in January 1992 when he was manager of West Brom, and will be at Taylor's special testamonial match against a Sir Bobby Robson XI.
At the start of this season, Taylor had scored 113 goals in 225 league starts for West Brom.