Jackett's in-form side are bidding for a Play-off place after an impressive run of just one defeat in their last 15 matches.
Wood has played an integral role in that run, scoring eight goals in 16 starts since making the temporary move from the Hawthorns in September.
That has alerted the likes of Leicester, who are also expected to submit a bid for the New Zealand international when the transfer window opens next month.
But Jackett is hoping to beat them to the punch for the 21-year-old, who is valued at over £1m by West Brom.
And that sum would beat Millwall's previous transfer record of £800,000, which was paid to Derby County for Paul Goddard back in 1989.
"We like Chris - he has done very well for us," said Jackett. "I think he has had two very good experienced partners alongside him in Darius Henderson and Andy Keogh, but he is a player we would definitely like to pursue once his loan expires.
"Would that be a permanent deal? Yes. We will have to see what January brings, but it is no secret that we like Chris and we would like to keep him here."