The 28-year-old midfielder is yet to sign a new contract at Montgomery Waters Meadow and is believed to be heading to Highbury Stadium to join the Cod Army.
Vela has spent two-and-a-half years at Shrewsbury but is now set to join up with another side closer to his north west home.
The former Bolton man held talks with boss Steve Cotterill at the end of the season, with his contract at Shrewsbury expiring at the end of this month.
Town confirmed yesterday it 'would appear' Vela is signing elsewhere. They claim there was an agreement on a two-year deal during talks at the end of the season.
Vela has been a regular in the side in his time at the club and was voted player of the season in his first full term.
In all he scored five goals in 94 appearances.
Shrewsbury’s retained list, published on May 3, said Vela has been offered and agreed new terms, to which Cotterill said “I’m delighted that we’ve agreed a new deal with Josh”.
But no fresh contract was signed and Town now find themselves another midfielder down as Cotterill continues with summer business. Jordan Shipley has already been drafted in from Coventry City.
Town's statement on the midfielder's imminent exit read: "Shrewsbury Town can also say that it would appear that Josh Vela will not be signing another deal with the club.
"Having agreed a new two-year deal with Steve Cotterill the day after the Wigan game, the club had his new contract ready at the start of May and sent it to him to sign.
"He then also subsequently agreed to sign the contract once again with Brian Caldwell after he returned from holiday."
Fleetwood, under the new management of Scott Brown, survived League One relegation by the skin of their teeth, ahead of Gillingham on goal difference.
Vela made his mark against his new side last season. He scored his goal of the campaign at Highbury in a memorable 3-0 Shrewsbury victory – their first on the road of the season in League One.
The energetic midfielder went on to score once more, again away from home, late on in the campaign. He scored at the Stadium of Light as Town were within seconds of a creditable point at eventual play-off winners Sunderland.
Meanwhile, Shrewsbury also confirmed that Elliott Bennett has signed a new one-year deal at the Meadow.
Telford-based Bennett, who signed last summer, made 48 appearances and was also revealed to have agreed new terms in the retained list.
The right wing-back, 33, said he was 'delighted' to extend his Town stay.