The forward has been heavily linked with a move to Norwich in January.
The Scotland international is expected to leave Goodison Park in the January transfer window; having found his game time significantly reduced this season.
He has started just four Premier League games so far this season, with the form of Romelu Lukaku and Arouna Kone having kept him out of the first team picture.
It had seemed he was set to join Norwich City, but that move has seemingly stalled, and now Swans boss Alan Curtis has confirmed they are interested in him.
"I think he's on a list [of transfer targets]," he told BBC Sport.
"I know he's a player available - he's an excellent player. Like all good players, if we can afford to bring him in, then we will be interested.
"We're still looking for that main striker. Steve is probably someone who plays just behind the main striker but someone we will be interested in."
Naismith would provide a boost to a side that has struggled for goals so far this season, a problem which has contributed to them now sitting just one point above the relegation zone.
Bafetimbi Gomis had started the season in fine form, but has struggled for the majority of the campaign while back up forward Eder is yet to truly get going at the Liberty Stadium.
They have managed just 19 goals in 21 league games this season, the second lowest of all the sides in the division, equal to bottom of the table Aston Villa.