The 25-year-old recently revealed that he has agreed terms with four Premier League clubs - Sunderland, Blackburn, Fulham and Tottenham Hotspur - adding that he was less hopeful of securing a dream move to Arsenal.
But Lyon chief Aulas, speaking at the presentation of new signings Michel Bastos - from Lille - and Porto defender Aly Cissokho, said he would also like to add the Ligue 1 hot-shot to the club's ranks ahead of the new campaign, but did not anticipate the forward leaving one French club to join another.
"When I see that Chamakh wishes to leave, but that people would authorise a departure to England but perhaps not France, it is regrettable," he said.
"Because we would be ready to welcome him with open arms."
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