The 25-year-old was the subject of a bid of £2.5million from Fulham manager Lawrie Sanchez last week which was dismissed as "derisory" by Saints.
Sam Alerted By Baird's Release
Baird can operate either at full-back or centre-back, and he shot to prominence as a shock inclusion in the Southampton side beaten by Arsenal in the 2003 FA Cup final.
He has two years left on his current contract and was named player of the year at St Mary's last season.