Bendtner was widely expected to depart the Emirates Stadium in the close season, and nearly sealed a move to Bundesliga outfit Frankfurt before the German club pulled out of the deal for financial reasons.
The 25-year-old is on the periphery of the Arsenal first team, with France international Olivier Giroud regularly chosen to lead the line, and spent the two previous seasons on loan at Sunderland and Juventus respectively.
Bendtner's only goals this season came when playing for Denmark in a 2-2 draw with Italy in October.
After seeing the forward make just three Premier League appearances this season, all from the bench, Olsen has told Bendtner to seek pastures new in the January transfer window in order to prolong his career.
"Bendtner scored two great goals for us in the game against Italy, but there were also things he lacked in the match and this only comes through playing games," Olsen told reporters.
"It is for this reason that he should find something new this winter. I think he will make the recommendation to himself and that is the main thing. Footballers want to play football.
"He has maybe 10 years left to go; he must use them well."
Bendtner will hope to gain a starting berth when Denmark host Norway in a friendly on November 15.