The 28-year-old was one of five players placed on the transfer list by Forest during the summer and failed to win a deal with Stoke after an earlier trial period at the Britannia Stadium.
He scored twice for Millwall in a recent behind-closed-doors game against Brentford but Lions boss Colin Lee told his club's website: "Alan hasn't played a great deal of football this season and consequently is lacking in match fitness so he's got some work to do in that respect.
"Once he's done that we might consider whether or not we think he could do a job for us."