O'Riley has scored 27 goals and provided 34 assists in 121 appearances since joining Celtic from MK Dons in January 2022.
Despite being a key part of Brendan Rodgers's side, there is some doubt as to whether O'Riley will still be a Celtic player for the 2024-25 campaign.
Atletico are continuing to keep tabs on the 23-year-old despite failing with a reported €21m (£17.8m) bid in the January transfer window.
At that point, Celtic's valuation was believed to be €29m (£24.5m), but AS are now reporting they have increased his asking price to €40m (£33.8m).
The report claims that Atletico will have to offload midfielder Saul Niguez before they pursue a summer move for the Celtic man.
With Atletico demanding around €20m (£16.9m) for the 29-year-old, they are hopeful that his sale can fund part of their bid for O'Riley.
Fenerbahce open Beto talks
Turkish giants Fenerbahce have reportedly interested in signing Everton striker Beto in the summer transfer window.
The Portuguese forward experienced a difficult first season in the Premier League after joining Everton from Udinese last summer.
Beto made just nine Premier League starts during the 2023-24 campaign, mustering three goals in 30 top-flight appearances.
The 26-year-old could now be offered a way out of Goodison Park, with Sabah reporting that Fenerbahce are showing an interest in the Everton man.
Fenerbahce have supposedly held initial talks to sign Beto as Jose Mourinho looks to bolster his forward options ahead of his first Turkish Super Lig season.
However, it remains to be seen whether the Toffees will be willing to sanction a sale just one year after signing Beto.
Trafford keen on Newcastle move
Burnley goalkeeper James Trafford is reportedly keen to complete a move to Newcastle United this summer.
The Magpies are looking to bring in a new goalkeeper to provide competition to Nick Pope, especially as their second-choice option Martin Dubravka appears to be heading towards the exit door.
Trafford has been identified as a potential target, with the 21-year-old likely to leave Burnley following their relegation from the Premier League.
According to the Newcastle Chronicle, Trafford is ready for a new challenge and is open to the prospect of joining Eddie Howe's side.
The report claims that Burnley are demanding £20m for Trafford after rejecting an initial £16m offer from Newcastle last week.
The Magpies are still hoping to make progress in negotiations but are willing to walk away if they fail to reach an agreement with Burnley.