"If teams like Barcelona lose games there is always a lot of critics, rumours, speculations," Koeman told reporters at Southampton's Staplewood training centre.
"And I know that, because my whole life I am linked to Barcelona," said the Dutchman who played almost 200 times for the Catalan giants between 1989 and 1995.
"But it is not a time to talk about that," Koeman added. "It is not respectful to the people of Southampton or Barcelona.
"I am very happy to be here. I started a contract in Southampton, and I like to respect my contract and the people."
Enrique this week was moved to deny growing rumours he had received an ultimatum from Barcelona officials, and insisted he has no problems with any player, including Lionel Messi.
Talk has been rife of disagreements between the pair, while Catalan radio reported that Chelsea had contacted Messi's father and agent Jorge about a possible move.
Barcelona, beaten by Real Sociedad last time out in La Liga, sit second in the standings, a point behind bitter rivals Real Madrid having played a game more. Remarkably, that could be said to constitute something of a crisis at the Spanish side, sparking the speculation.
Koeman meanwhile leads his fourth-placed Southampton into battle against third-placed Manchester United in an English Premier League showdown on Sunday.
(Editing by Justin Palmer)
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