Graham was stretchered off early in the second half of United's 1-1 draw away to Inverness on Sunday with ankle ligament damage.
Now McNamara, who moved to bring in forward Farid El Alagui on loan from Brentford last week as David Goodwillie made his way back to Blackburn Rovers, could be ready to delve into the transfer market again to ease his striking shortage.
"It's a shame for Brian because he's been getting a run of games but there's nothing you can do about that kind of injury," said McNamara.
"It's just as well we brought Farid in when we did. He did well when he came on against Inverness and will be a good player for us.
"I was looking at other areas but we'll have to see what happens with Nadir [Ciftci]. I don't think his groin is as bad as we first thought."
United are also hopeful of securing influential duo Mark Wilson and John Rankin on extended deals soon.