Liverpool were also in the running to sign Chamakh, who has reportedly agreed a £50,000-a-week four-year deal with the Gunners.
“We looked last summer at Chamakh and he’s a very good player – he would have been a great addition to the squad,” Bruce told the Sunday Sun.
“We tried to sign him but it was a non-starter really, because Bordeaux didn’t want to sell. They wanted to keep him this season, play him in the Champions League and possibly see if he would sign a new deal with them.
“We were never really that close to signing him because we never really got near agreeing a fee with Bordeaux – they said he wasn’t for sale.
“If he’s gone on to sign for Arsenal, that shows how good he is and we wish him the best of luck.
“He’s a very good striker who will relish playing at a club like Arsenal.”