Johnson, who swapped Oakwell for Ashton Gate in February, is said to be courting players from his old club and Preston North End.
Bristol City boss Lee Johnson
Johnson swapped Oakwell for Ashton Gate in February and achieved his remit of keeping the Robins in the Championship.
In his absence, Barnsley made a late surge towards the League One play-offs, and were promoted on Sunday under the 34-year-old's temporary successor Paul Heckingbottom.
Despite this, Johnson reportedly has his eyes on three Tykes stars ahead of his first full season as City boss.
Barnsley's Adam Hammill celebrates with the man of the match trophy after winning the Sky Bet Football League One Play-Off Final
Winger Adam Hammill, who scored the Yorkshire side's stunning second goal in their 3-1 play-off final victory against Millwall, centre-back Alfie Mawson and on-loan midfielder Josh Brownhill are all said to feature on their former boss's list of targets.
And the report claims that Johnson, who spent 12 months at Oakwell, is keen to reunite with his former Oldham and Barnsley assistant Tommy Wright.
Barnsley manager Paul Heckingbottom and assistant manager Tommy Wright celebrate with the trophy after winning the Sky Bet Football League One Play-Off Final
Both Hammill and Brownhill, who the Robins boss borrowed from Preston North End in January, are both available on free transfers this summer, though Mawson would command a fee.
Josh Brownhill celebrates after scoring the third goal of Barnsley's play-off victory against Walsall