The 33-year-old has only been offered a six-month deal by current club Kilmarnock and is keen to get a better offer elsewhere if possible.
Slade is aware of McSwegan's abilities having worked with him at Notts County in the mid-90's.
The twice capped Scot has never really succeeded in the English game, but has found reasonable success in Scotland.
Reports in Scotland claimed Slade had offered a two-year contract, Slade denies this but admitted he is interested in the former Barnsley striker.
"Gary is a player I worked with at Notts County and he is certainly one on the long list of players I am interested in," he told the Grimsby Telegraph.
"But there is definitely no truth in reports I have offered him a deal - I don't know where that has come from."