The Premier League champions have already signed Gael Clichy, Samir Nasri and Bacary Sagna from the north London club and were hoping to make it fourth time lucky with a move for the England star.
But the Arsenal manager is adamant that Wilshere, who has only just returned from a long-term ankle injury, will not be going anywhere at the end of the season and remains a key part of their long-term plans.
Wenger said: "You can imagine my answer, we are not in a position anymore where we have to sell our best players.
"We cannot make a headline from anything in a press conference from something which is not true."
