Guido Albers is the Dutchman's former agent and manages ex-Inter boss Frank de Boer.
In an interview with Italian media this week, he rejected the possibility that De Boer could be an option for Barcelona, but suggested Koeman is one of the managers they have in mind.
Current Barca boss Luis Enrique has enjoyed significant success at Camp Nou but is out of contract at the end of the season.
But Koeman dismissed Albers' claim and suggested links with Barcelona are inevitable given he has had spells with Barca as a player and assistant manager.
"He is not my manager anymore," Koeman said ahead of Saturday's Premier League game at Middlesbrough.
"[There is] nothing, nothing, nothing. I will always be related to Barcelona - it happened in the past and it will happen in the future."
Everton have been tipped for a shock top-four finish as they sit seventh after picking up 17 points from a possible 21.
But Koeman is not getting carried away and will not take struggling Boro, who are without a win in seven top-flight matches, lightly.
He added: "Everything is possible but everyone knows the Premier League is so tough.
"Maybe our game this Saturday will be more difficult than Tottenham away. It is all about yourself. The best way to be successful is to look at the next game.
"They are fighting for the points to stay in the Premier League and that can be really tough when teams are fighting for their lives. Sometimes it can be harder than against teams in the top six."
Koeman also insisted James McCarthy was never on the transfer list despite the midfielder being linked with a move away after the signing of Morgan Schneiderlin.
He said: "No [McCarthy has not had to win me over]. All that is speculation.
"From the beginning he was an Everton player and I did not change my mind. He was not at the right fitness in the beginning. He had a difficult time.
"But now he has really showed his qualities. When his fitness is really good he is an important player and most of the time he has started the games. That is the best you can show a player as a manager – starting him.
"He was never on the list to leave Everton. That is all rumours in the press, but not from inside."