The 32-year-old Northern Ireland international, who can play in midfield and across the back four, spent four months with the Royals earlier this campaign.
Reading were unable to keep hold of the former Fulham player due to financial reasons, however, and after leaving the club in January he was signed by Burnley until the end of the season.
"He trained with us on Tuesday, so he had been with us regularly," Adkins is quoted as saying by Get Reading. "The idea is that we would have been in a situation where he could have stayed with us at least until the end of the season, but that's not materialised.
"We wish him well because he did really well in the time he was here with us. But likewise he's not been getting paid since January and he can't hold on forever [for a contract], can he?
"It's funny how things work out because all of a sudden he's got a chance to be involved with a team and get to the Premier League."
Baird made nine appearances in his spell at the Madejski Stadium.