It is understood that the 32-year-old has emerged as a target for the Lilywhites who have made an enquiry regarding his availability.
Despite contacting the Robins to find out what it will take to sign Wells on a permanent deal, Preston have yet to submit an offer for him.
Wells has yet to report for pre-season at Bristol City as he was handed an extended break by the club after representing Bermuda in their Nations League clashes with Haiti, Guyana and Montserrat.
Due to the presence of Antoine Semenyo, Andreas Weimann and Chris Martin, the striker was utilised predominantly as a substitute last season.
Wells only started in seven of the 32 league games that he participated in for the Robins as his side meandered their way to a 17th place finish in the Championship standings.
Preston made their first signing of the summer transfer window as they secured the services of Freddie Woodman on a permanent deal from Newcastle United.
The goalkeeper put pen-to-paper on a three-year deal which will keep him at Deepdale until 2025.
When you consider that Wells’ current deal at Ashton Gate is set to expire in 2023, the Robins may be open to the possibility of letting him leave this summer if Preston submit a reasonable fee for him.
Whereas the striker only managed to find the back of the net on three occasions for his side last season, he has demonstrated in the past that he is more than capable of delivering the goods in the Championship.
Providing that Preston are able to negotiate a deal for Wells, this may turn out to be a good bit of business by the club as he could potentially thrive under the guidance of Ryan Lowe who featured in the same position as the former Bradford City man during his playing career.