Targets Julien Dacosta, a right wing-back from Coventry City, and Preston North End midfielder Tom Bayliss are down the line with talks to become summer signings number two and three at Montgomery Waters Meadow.
Manager Steve Cotterill has been eyeing additions in those positions as he continues his recruitment drive. Town are also looking at centre-forward and left wing-back recruits.
Bayliss, 23, is available to sign from Championship outfit Preston, where he has 12 months left on the four-year contract he signed for a reported £2million in 2019.
North End are working to cancel his contract so Leicester-born ex-Coventry man Bayliss can move on.
He is described as a midfield playmaker with a good engine capable of travelling comfortably with the ball. Bayliss, who only played 21 times in all competitions for Preston, spent last season on loan at League One champions Wigan – and made 16 appearances, eight in the league.
He adds required competition and depth in Town's midfield alongside Luke Leahy and the sole new recruit so far this summer Jordan Shipley, the May arrival from Coventry. Josh Vela left Shrews lighter in that department with his exit to Fleetwood.
It is possible the 2022/23 campaign could also see vice-captain Elliott Bennett, who signed a contract extension, become a more regular option in the middle of the park due to the pursuit of wing-back Dacosta.
The Sky Blues' 26-year-old Frenchman has been on Cotterill's radar for some time and was was very close to moving to the Meadow on loan in January, but he opted on a loan to Portugal outfit Portimonense at the 11th hour.
Cotterill and Shrewsbury retained their interest in the Coventry man, however, and the club hope to have got their man, who is expected to finalise a season-long loan deal as the squad begin the hard yards of pre-season before jetting out to Spain for a warm-up camp on Saturday.
Dacosta is a direct and attacking right wing-back and would provide sought after competition to Bennett on that flank.
He made 11 appearances for Portimonense in the second half of last season after Town thought they had sealed a loan deal. He has one more season to run on his contract at Coventry, which expires next summer.
Marseille-born Dacosta moved to English football with Coventry in 2020 from French second tier outfit Chamois Niortais. He made 24 appearances in all competitions for Coventry.