Townsend impressed on loan at The Den last season and signed a new contract at Tottenham on Thursday.
The Lions boss told the New Shopper: "I don't know what the situation is.
"We have been making a lot of enquiries and at the moment I don't know anything in terms of Spurs' options.
"I'm sure there are lots of clubs, and we are one of them, jostling for position on players.
"We are looking to strengthen in January, definitely. We will have to see which positions, but we do think we need to improve."