O'Riley has been heavily linked with a move away after impressing with 19 goals and 18 assists in 49 competitive appearances last season.
The midfielder has attracted interest from Chelsea, Southampton and Brighton & Hove Albion, but is Atalanta who have made a considerable effort to secure his signature.
The Italian club have seen multiple bids rejected by Celtic, denting their hopes of signing the 23-year-old this summer.
However, according to Football Insider, Atalanta are not willing to give up on their pursuit and are ready to submit a fresh proposal.
The report claims that Celtic are holding out for £25m for a player who is under contract until the summer of 2027.
The Scottish champions are still keen to retain O'Riley's services, especially as they prepare to compete in the new eight-game league phase of the Champions League.
Brentford making progess in Nunes pursuit
Meanwhile, Brentford are reportedly leading the race to sign highly-rated winger Gustavo Nunes from Brazilian side Gremio.
The Bees have made a couple of additions this summer, having signed forward Igor Thiago and attacker Fabio Carvalho from Club Brugge and Liverpool.
Despite recruiting Thiago and Carvalho, Brentford are still seemingly keen to bolster their attacking options with the addition of Nunes.
According to journalist Fabrizio Romano, the Bees have sent a fresh bid for Nunes after failing with their initial proposal.
The update claims that Nunes has turned from offers from the Saudi Pro League and is keen to complete a move to the Premier League, leaving Brentford in pole position to secure his signature.
Nunes, who graduated from Gremio's youth system, has scored six goals and provided four assists in his 38 appearances for the first team.
Chelsea sell Moreira to sister club
Over at Chelsea, they have confirmed the permanent sale of Diego Moreira to their sister club Strasbourg.
After joining Chelsea from Benfica last summer, Moreira was sent on loan to French side Lyon, where he made just nine competitive appearances before he was recalled in January.
Moreira has now returned to France after Chelsea confirmed they have sold the attacker to Ligue 1 outfit Strasbourg for a reported £1.7m.
According to the Standard, Chelsea have included a buy-back clause in a deal which has been made as a workaround to a regular loan move.
Strasbourg, who are also owned by BlueCo, have already signed two players on loan from Chelsea this summer, recruiting Caleb Wiley and Andrey Santos.
As a result, they can only recruit one more player on loan from their sister club and there is a possibility that Djordje Petrovic could fill that spot.