HITC Sport understands several clubs are tracking former Ipswich Town forward.
Ipswich's Luke Varney celebrates after he scores their third goal
Former Leeds and Blackpool ace Varney is currently a free agent after seeing out his contract at Ipswich earlier this summer.
Varney signed a short-term deal at Ipswich last December after recovering from an Achilles injury he picked up while on loan at Ipswich the previous season in the play-off semi-final first leg against rivals Norwich
The versatile forward scored one goal in 20 appearances for Ipswich last season, but Town boss Mick McCarthy opted not to offer him a new deal as they already had four strikers on the books at Portman Road.
Luke Varney during Blackburn training
Varney is an attractive proposition for his suitors as he boasts a wealth of experience having played the majority of his career in the Premier League and Championship.
Varney, who came to the fore at Crewe, has made over 350 appearances in his career to date having enjoyed spells at Charlton, Derby, Sheffield Wednesday, Blackpool, Portsmouth,. Leeds, Blackburn and Ipswich.
Varney's experience and versatility has alerted several sides as they look to bolster their attacking options before the start of the new season.
Blackburn Rovers' Luke Varney in action with Leeds' Jason Pearce