27-year-old Cureton is familiar with West Country football, having been a former Bristol Rovers player before moving to The Royals in a £250,000 move in August 2000.
Cureton has been offered a new one-year deal at The Madejski Stadium but his desire for more first team action has seen the Bristol-born hit-man consider offers in Korea and the United States, having accepted a trial at Major Soccer League side DC United last week.
Robins chairman Steve Lansdown has dismissed any thought that a move for free agent Cureton is linked with Reading's increasing interest in winger Scott Murray and sees both players being part of the same Ashton Gate squad next term.
"If we could add someone of Jamie's quality and keep Scott, it would give us enormous potential for scoring goals," Lansdown told the club's official website.
"He is one of a few players we have inquired about and we have talked with his agent to establish the early position."
The Ashton Gate club's pursuit in signing Cureton may face stiff competition from QPR boss Ian Holloway, with the former Bristol Rovers manager confirming he will try to make an offer for one of his former charges next week.
"I'm looking to bring in attack-minded players and I would like to make an offer for Jamie Cureton next week," Holloway told QPR's official website.
"I've worked with him in the past and hopefully no-one will spoil it.
"He is an ambitious lad and would like to play in The Premiership again, but I believe we have a chance because he knows what he's getting from me.
"After everything that's happened to him, he's matured and I enjoyed seeing him again and talking to him."
Meanwhile, Bristol City have also revealed that they have rejected a new offer from The Royals and an unnamed Division One club of a cash-plus-player deal for Murray.
The Robins initially rejected Reading's first offer of £500,000 for the Scotland B international and Lansdown has insisted that their cash valuation of the winger is more of a priority to the club.
"The latest offer from Reading does include a player, but the cash included in the deal has dropped slightly, I assume in accordance with Reading's valuation of their player," added Lansdown.
"The cash value of any deal is the most important thing to us and for that reason we have rejected the latest bid from Reading, as it is still some way short of our valuation of Scott."
