Martial is set to miss the clash with Jose Mourinho's revitalised Spurs because of a muscular injury he sustained against Aston Villa.
Martial was substituted after 82 minutes of Sunday's 2-2 home draw with Villa and reports claim he has been ruled out.
Solskjaer looks likely to once again adopt a formation featuring three central defenders, as he did late last month when his side drew 3-3 against Sheffield United.
Harry Maguire, Victor Lindelof and Phil Jones started together for that match, but Jones was subsequently dropped from the squad for the Villa match and fit-again Axel Tuanzebe may get the nod instead.
Solskjaer has already ruled out Paul Pogba and stated that both Scott McTominay and Nemanja Matic are "touch and go" to face their former manager's new side.
McTominay has missed three games with an ankle complaint, while fellow midfielder Matic has not played for two months with an unspecified issue.
Pogba remains out as he recovers from an ankle injury, while Eric Bailly, Timothy Fosu-Mensah and Diogo Dalot continue to build fitness.
Mourinho is expected to freshen up his starting line-up again for the trip to Old Trafford and could recall Lucas Moura, who started his first two matches in charge.
Harry Winks missed out against Bournemouth, as Spurs again won 3-2 on Saturday, after struggling against Olympiakos and will be hoping for another chance in midfield.
Danny Rose could be drafted back in at left-back unless Mourinho decides that Jan Vertonghen should continue there after switching him from centre-back at the weekend.
Erik Lamela and Michel Vorm, who are still battling respective hamstring and calf injuries, continue to be unavailable for Spurs.
Hugo Lloris (elbow) and Ben Davies (ankle) remain long-term absentees.