It follows on from the news that Sheffield United are hoping to link playmaker James McAtee up with Tommy Doyle.
The story of 22-year-old Tedic is a familiar tale in an era when big clubs increasingly swallow up young talent.
Having impressed in his native league with Cukaricki, Tedic was snapped up by City in 2020, but is yet to play for them, instead spending two years on loan in the Netherlands with limited success.
All his three goals for Zwolle came in 2020-21, and he failed to find the net in 23 matches last season as they finished bottom of the Erediviside.
Nevertheless, Barnsley clearly see something in the striker, and are in need of firepower after losing Carlton Morris and captain Cauley Woodrow to Luton Town after relegation to League One. Victor Adeboyejo, George Miller (who joined Doncaster Rovers) and Patrick Schmidt also left on free transfers.
Barnsley scored 33 goals in 46 Championship matches last season - a Football League tally bottom-of-League Two Scunthorpe United failed to better.
James Norwood joined from Ipswich Town, but so far new manager Michael Duff's main focus has been on the team's defensive foundations. Even in that area there could be more high-proifle departures, with reports of Lech Poznan having a £1.5m bid for Polish centre-back Michal Helik accepted.
Helik did not feature on the opening-day defeat at Plymouth Argyle, with the club reporting a minor thigh strain.
Midfielder Doyle joined the Blades from City in the summer, although he too was missing from their opening game through injury.
Although manager Paul Heckingbottom claimed ignorance to stories circulating before the 1-0 defeat at Watford about McAtee's imminent arrival, he did acknowledge and spoke freely of his admiration for the 19-year-old England under-age player who, like Doyle, has played first-team football for the Citizens.
Reserve goalkeeper Zack Steffen, who is 27, has joined Middlesbrough on loan from City, and made an impressive debut in the 1-1 draw with West Bromwich Albion.
Under new FIFA rules to prevent the "hoarding" of players, clubs will only be able to loan eight out at a time but it does not apply to under-21s or anyone who has spent three years in that league between the ages of 15 and 21.