Hammers make Chamakh approach
The Moroccan forward, 28, has struggled to claim a regular place in the Gunners' first team after initially impressing following a free transfer from Bordeaux in 2010.
"We have made an enquiry and that is all we have done at the moment," said Allardyce. "From my point of view, the situation I have with Andy Carroll being injured and Modibo Maiga going to the African Nations Cup, means as a striker we have Carlton Cole and that is it until Andy gets fit."
He added: "If it is a possibility that it could be a deal done, then we are looking at it, as well as a number of others.
"We need to find a left-back as quick as we can as well, because Joey O'Brien has a hamstring problem and George McCartney is out for a number of weeks, so we will have to see if there is anyone who we can find in that position for us."
Allardyce said: "I did not know Martin was available, so we will have to wait and see if they make Martin available at Blackburn. I would definitely be interested because I worked with the lad when I was at the club and helped develop him into what I consider now to be quite a good player.
"Whether Blackburn are wanting to sell anybody in their fight to get back into the Premier League, I don't know."