Bendtner watched Copenhagen give up a lead at Parken, the club's home ground, to draw 1-1 with Randers and it sparked rumours that the 26-year-old could head home to resurrect his career with the reigning Danish champions.
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"We are not talking about that," Horsholt told reporters.
"[Bendtner] is in town and is an old Copenhagen boy, who during his childhood days [attended games at Parken]. He wanted to see some football, it isn't anything more than that.
"Unfortunately we couldn't give him a win."
Bendtner was pictured alongside Horsholt and Frank Arnesen, the sporting director at Metalist Kharkiv in Ukraine, who used to work for Hamburg, Chelsea and Tottenham.
It is widely expected the Danish forward will leave Arsenal at the end of the current campaign, having played just nine Premier League matches so far this season.
Late last year, Bendtner revealed he would be interested in returning to his home-town club at some point in the future.
"I like the idea of finishing at FC Copenhagen and try the Superliga at the end of my career," Bendtner told Danish newspaper Politiken.
Bendtner signed for Arsenal from Kjobenhavns Boldklub in 2004, one of two clubs that merged their professional teams to form FC Copenhagen in 1991.