Lansbury suffered a nasty knock at Bristol City on Monday but Mackay hopes to sign him up until the end of the season.
Mackay said: "Henri has twisted his ankle; the medical department will be keeping an eye on him in the next couple of days, but he has ice on it now so we will just have to see.
"It's a nasty ankle injury.
"But we've already opened talks with Arsenal about extending the lad's stay with us and I don't expect that decision to be affected.