Having enjoyed somewhat of a resurgence under Rowett since the turn of the year, Millwall appeared in line to make a late charge for the top six.
However, Saturday's 2-1 reverse at Barnsley has extended the Lions' winless run to three matches, a period which they could ill-afford if they want to challenge for a Premier League place.
A lack of goals has been a problem all season, and Rowett has been left disappointed with just two strikes coming in fixtures against Wycombe Wanderers, Luton Town and Barnsley.
There is a feeling that victory on Tuesday evening could help turns things around for Millwall, particularly with a batch of favourable matches to come before the next international break.
Nevertheless, Millwall will drop several places down the table if results go against them in midweek, strengthening the argument that they must go on the front foot against Preston.
Neil will feel obliged to do the same with the visitors, who comfortably dispatched Huddersfield Town by a 3-0 scoreline at the weekend.
The North-West outfit had also looked devoid of confidence in the final third, and few players could have argued if they had been dropped for the meeting with the Terriers.
Beating the worst-performing team in the division will not be enough to encourage Neil in the long term, but the Scot will at least feel that his side now have the firepower to get the better of a tough Millwall backline.
Millwall Championship form: WWWDDL
Preston North End Championship form: LWLLDW
Rowett will make several changes to his Millwall XI with top goalscorer Jed Wallace potentially being handed a rest.
Barring any late fitness issues, Neil is expected to stick with the same side which started Preston's fixture against Huddersfield.
Millwall possible starting lineup:
Bialkowski; Hutchinson, Pearce, Evans; Romeo, Woods, Williams, Malone; Bennett, Smith, Bodvarsson
Preston North End possible starting lineup:
Iversen; Van den Berg, Storey, Hughes, Cunningham; Browne, Whiteman; Sinclair, Potts, Gordon; Evans
We say: Millwall 2-1 Preston North End
With no immediate threat of relegation for these two clubs, there is no reason why they cannot throw caution to the wind on Tuesday. While Preston are capable of scoring goals away from home, we think that Millwall are better equipped to claim all three points in a hard-fought match.