Stevenage chairman Phil Wallace admits midfielder Michael Bostwick is likely to be playing in the Championship next season.
Peterborough are understood to be one of a number of second-tier clubs tracking the 24-year-old, who has made 194 appearances in four years with Boro.
Wallace told Stevenage's official website: "Michael Bostwick has been on the radar of several Championship clubs.
"A situation is quickly developing whereby the policy of the club is being met to allow lads to move upwards.
"He's given four years of outstanding service to Stevenage and although we have made him a fantastic offer to sign a new deal, I fully understand that interest from Championship clubs may make it the right time for Bossie to move up."