Alan Irvine says he has no deals in the pipeline that he expects to be completed before West Brom's next outing.
Victor Moses claims to have had 'a few other options' to consider when making the decision to join Stoke on loan.
The 29-year-old, who made 153 appearances for the Gunners from 2004 to 2008, returns to the Emirates Stadium after five seasons in Serie A with AC Milan, having become a free agent earlier in the summer.
Arsenal manager Arsene Wenger is confident versatile Flamini - who played at left-back in the 2006 Champions League final defeat to Barcelona - will settle quickly into life back at his old club, having spent some time training at their Hertfordshire base this month.
"We are very pleased Mathieu has agreed to rejoin us," Wenger said on www.arsenal.com.
"He is a player of real quality, with a fantastic work rate and great mentality.
"As we know, Mathieu is a strong midfielder, but is also is comfortable playing in defence too. He is a very good addition to our squad."