New Robins boss Steve Coppell has deemed the 33 year old surplus to requirements at City and won't be offering him a new deal.
Trundle scored five times for Swansea last season, making him the club's joint second highest scorer, behind Darren Pratley who finished with seven.
The Scouser managed to score every 104 minutes in the Championship in the past campaign – the best goal to minutes ratio in the division.
Paulo Sousa is due to sit down and discuss the futures of all his players at the end of this week and Trundle has offered to take a paycut in order to keep his place at the Liberty Stadium.
An announcement is likely early next week to confirm the fate of a number of out of contract players including the likes of Cedric van der Gun, Fede Bessone and Jazz Richards.
This article first appeared on JACKARMY.net.