Arsene Wenger finally secured the signing of Moroccan international Chamakh last month having been chasing the goal-getter for a year.
And the Emirates Stadium supremo, who has been in South Africa working for French television, is on the lookout for more new recruits ahead of the 2010/11 campaign.
Lorient defender Laurent Koscielny is believed to be close to joining Arsenal, with fellow stoppers Sol Campbell, William Gallas and Mikael Silvestre on their way out of the Gunners and Philippe Senderos having already signing for Fulham.
And Wenger is widely expected to be without captain Cesc Fabregas' services next season, with the Spanish midfielder tipped to return to Barcelona after the World Cup finals.
French midfielder Gourcuff, who along with Chamakh guided Bordeaux to a first league title in 10 years in 2008/09, is already back in his homeland following France's dismal displays in South Africa.
He was sent off in the final group game against South Africa.
Chamakh has revealed that, should Fabregas seal his switch back to Catalunya, Gourcuff would be an ideal replacement, despite the fact that the former AC Milan playmaker will not be available on the cheap.
"It would be terrific if Gourcuff joined Arsenal," he said in The Sun.
