According to Bouchette, there is a chance that an agreement could be in place at some point this week.
Gilbert, 26, is entering the final year of his rookie contract and is set to make a base salary of $815,103 for the 2014 season.
The Steelers used a second-round draft pick on Gilbert back in 2011. Since then, he has appeared in 35 total games for Pittsburgh and played a total of 965 snaps last season.
Pro Football Focus has him rated as the No. 50 offensive tackle out of 76 qualifying players last season. He had negative ratings in both run and pass-blocking, according to PFF.