Austin, who has scored 17 goals for the Robins this season, has asked for a move away from the Robins amid interest from Championship clubs.
He joined Swindon from non-league Poole Town in October 2009.
Since then he has found the net 37 times in 65 games and signed a new two-and-a-half-year deal in February 2010.
Robins boss Danny Wilson revealed on Wednesday that
Blackpool had made an offer for the frontman.
"As far as we're concerned there is one offer that is fairly close and that's Blackpool," he told BBC Wiltshire.
Source: BBC Sport
Source: BBC Sport