The Swans, along with Championship leaders Wolves, have been tipped to make a move for the London-born Ghana international this month.
Adomah is Villa's top scorer this season, with 12 goals in all competitions, and manager Steve Bruce has ruled out a January exit for the 30-year-old and his other key men.
"What I don’t want to do is sell anybody who is a value to us right now," he said.
"In the summer, we had to get rid of players like Jordan Amavi, for instance. In an ideal world, we didn’t want Amavi to go but the offer [from Marseille] was too good for us, and it enabled us to do what we needed to do.
"It’s not easy with FFP [Financial Fair Play], but I don’t think we would lose one of our better players in January."