Rice recently signed a new rolling contract with the Accies, where he has served as manager since 2019. However the Lanarkshire club’s seven year stay in the SPFL Premiership ended at the weekend when they were relegated to the Championship.
Falkirk have been seeking a new manager since sacking co-managers David McCracken and Lee Miller on April 21 as the Bairns slipped off top spot in League One. The change failed to arrest their slump and the Bairns ended up missing the play-offs with director of football Gary Holt taking interim charge of the remaining six games.
Holt has returned to his sporting director position and is leading the search for a new manager but, according to the BBC, has been rebuffed in an approach to speak to the former Bairns player and assistant manager Rice, who played at Brockville from 1991 to 1995, making more than 100 appearances.
He was also assistant boss to former Falkirk team-mate Ian McCall and stayed on to assist another, John Hughes, at the Bairns.
Another former player, Neil McCann, was also reportedly sounded out over the job following his departure from Inverness, but the ex-winger turned down the opportunity to discuss the vacancy – although the club has stressed no job offer was made.
Falkirk say more than 100 applications were received for the job – with names including Darren Young, Stuart Taylor and Peter Grant also linked to the post.