The 23-year-old has been the subject of much speculation over the last 12 months since established himself as a first-team regular for the Hoops.
Sky Sports News claims that La Liga leaders Girona have expressed an interest in signing O'Riley and have been monitoring the midfielder's progress throughout this season.
Serie A giants Inter Milan have previously been linked with O'Riley and it is thought that they could swoop for the Denmark international if they agree to part ways with Leicester City-linked Stefano Sensi.
A host of other European clubs are said to have sent scouts to watch O'Riley, who has scored 10 goals and registered 10 assists as a centre-midfielder in 28 games for Celtic across all competitions this season.
Rodgers has since addressed the speculation surrounding the future of O'Riley, who extended his contract with Celtic in September last year until the summer of 2027.
Asked at a press conference on Friday ahead of Celtic's Scottish Cup tie with Buckie Thistle on Sunday if he is aware of any interest in O'Riley, he said: "None. I'm not aware of any. But it is natural if you have good players they will attract attention. I'm not focussed on that at all."
"The club is in a really strong position," Rodgers added. "We have no need to sell, and we have no thoughts of selling. The plan was to add to the squad and that's still the plan.
"Naturally it's the time of the season where there is a lot of speculation and gossip around players. I see the likes of Matt and he is really, really happy here.
"He has signed a new deal. He has really progressed and is in double figures with his goal and his assists are there.
"For him as a young player, as a brilliant professional all he wants to do is improve, and you can see the improvement. We just take it day by day and assess it from there."
It is thought that Celtic would demand a Scottish-record transfer fee for O'Riley, which would be a figure in excess of the £25m the Hoops received from Arsenal for Kieran Tierney in 2019.