The Moroccan's 13 goals last season helped secure a first league title in 10 years for les Girondins, but he has since made no secret of his desire to leave the Stade Chaban Delmas.
Chamakh has claimed to have agreed terms with Sunderland, Fulham, Blackburn Rovers and Tottenham Hotspur, adding that he would prefer a move to Arsenal.
However, after the Gunners saw a €7 million bid for the front-man rejected, Wenger insisted he would not be increasing his offer nor his efforts to sign the striker, stating he would rather wait a year and land the front-man for free.
Recent reports have suggested that Bordeaux have lowered their asking price for the forward down to €12 million from €18 million.
But the Frenchman insists he has not wavered fom his original stance, leading former Manchester United defender Blanc to question the Gunners' genuine desire to sign the striker.
"Do Arsenal really want Chamakh? It is exactly the question that I ask myself and I believe no," he told France Football.
"Frankly, I believe if they really want him, he could join them within 48 hours.
"I would like him to stay. Early last season I told him, when he already wanted to leave for England, 'Have another good season with us. If you score between 10 and 15 goals, you will be in a strong position to leave for a big club'.
"I gave him my word and I told him I would let him leave. I am keen to respect what I said."
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