The 28-year-old Welshman could be on the way out of Championship outfit Cardiff City, despite playing 40 times for the Bluebirds in all competitions last campaign.
It is understood Vaulks is interested in a move to Darren Moore’s side, who missed out on promotion in the play-offs after defeat to Sunderland, despite the club being in the third tier of English football.
The Star reports that he is a main target for the boss, with talks having already taken place regarding a potential move.
It is said he has an appreciation for the ‘size and history’ of Wednesday, which ‘could play its part’ in his decision.
The all-action midfielder made a name for himself at the Bairns, making over 100 appearances for the club before moving on to Rotherham United.
He joined in February 2013 having been released from Tranmere as a youngster but was determined to prove his worth even if he was just earning 33p a week.
In his time at Falkirk his determination, skill and endeavour endeavour made him a true fans’ favourite.
“I look back at Falkirk with nothing but happy memories. It was some of the best times of my career,” Vaulks said of his old club previously speaking to the Herald.
"It’s the first result I look at, along with Rotherham, I always look out for my old teams and Falkirk’s a team that will always be close to my heart.
"I know a lot of players say this about their old teams but the way my Falkirk career went and how I felt so close to people in the area, I loved it straight away.”