Celtic have rejected Atletico Madrid's bid for O'Riley, Rodgers confirms
Rodgers claimed Atletico's offer for O'Riley was well short of Celtic's valuation, but the Scottish champions will not sell regardless of the financial incentive.
Atletico targeted O'Riley after he impressed against them in this season's Champions League group stage.
Celtic's lead at the top of the Scottish Premiership was cut to five points by Rangers' win over Hibernian on Wednesday with the Ibrox club still holding one game in hand.
And Rodgers is keen to emerge from the transfer window with a stronger squad rather than a weakened one.
"Matt is a player we don't want to lose and he won't be going anywhere in January," Rodgers told reporters on Thursday.
"It's a great testament to him and what the club can do for a player. He won his first international cap this season and Atletico Madrid are a big club in European football.
"But he is very much part of what we are doing. He has been a joy to work with and I had a good chat with Matt and he is someone who will be here for us in the second part of the season."
O'Riley, signed from MK Dons in 2022, is pushing for a place in Denmark's Euro 2024 squad and appears happy to continue developing at Celtic.
He has produced 10 goals and 12 assists this season and recently extended his contract until 2027.
"He had an opportunity in the summer but he was very happy to extend here and obviously Atletico Madrid is a huge club but he also knows he is in a great place here," Rodgers said.
"Firstly, you have a value of the player and certainly what has come in for Matt in the time I have been here is nowhere near the valuation of the quality of player he is.
"But even if it was we are in a position where we don't want to sell."