Belgian media reported that Belgium coach Dick Advocaat would replace his Dutch compatriot at Alkmaar for the rest of the season while continuing with his national team job.
The Belgian FA was not immediately available to comment.
Koeman, 46, joined Alkmaar in June 2009, after Louis van Gaal moved to Bayern Munich.
His team won the Dutch Super Cup but failed to reach the Champions League knockout phase this season from a group including Olympiakos Piraeus, Arsenal and Standard Liege.
Alkmaar have to win at Standard Liege in their last Group H match to finish third and qualify for the Europa League.
Alkmaar lost 2-1 at home to Vitesse Arnhem in the Dutch championship on Friday, their seventh loss in 16 league matches, leaving them sixth, 16 points behind leaders Twente Enschede.
Belgian TV programme Sporza reported on its official website on Sunday that Advocaat would take over from Koeman, who was also sacked by Valencia in April, 2008.
Advocaat was appointed Belgium coach two months ago after a spell at Zenit St Petersburg where he won the Russian title and UEFA Cup and he will continue in that role, the report said.
Advocaat took up the Belgium job three months earlier than planned after being sacked by Zemit following some disappointing results. Belgium failed to reach the 2010 World Cup finals.
