With Danielle Dichio suspended and Bob Peeters out for the rest of the season, Mark McCammon was set to make his first start in ten months alongside Neil Harris but the former Brentford hitman has fallen ill with swollen glands.
That means Wise has two possible options left. Kevin Braniff is now favourite to start upfront with Harris but the pair have failed to gel in previous games, which leaves the untried John Sutton, who recently signed from Raith Rovers.
Although Sutton has sixteen goals to his name already this season from his stint at Stark's Park, Wise sees him as one for the future and his Lions career so far has been restricted to just one brief substitue appearance against Crewe Alexandra.
Tim Cahill could also play up front for Millwall, but Wise is keen to retain the diamond formation that has proved so successful over recent weeks.
Burnley, meanwhile, have their own selection problems, with both Paul Weller and Tony Grant suspended, ironically thanks to cards picked up a fortnight during the two sides' Fifth Round FA Cup clash.