Davies has an ankle problem suffered before the recent international break.
Fellow full-back Doherty's muscle injury, sustained while away on Republic of Ireland duty, also keeps him out.
Boss Jose Mourinho has no other selection concerns as his side try to get their Champions League hopes back on track.
Rashford had been a doubt for Thursday's Europa League tie at Granada but scored and lasted 65 minutes before being taken off to protect an ongoing ankle complaint.
Shaw came off at the break with an unspecified issue that Solskjaer hopes will not rule him out of the trip to Spurs, which Anthony Martial, Phil Jones (both knee) and Eric Bailly (Covid-19) will miss.
Tottenham provisional squad: Lloris, Hart, Aurier, Tanganga, Dier, Alderweireld, Rodon, Sanchez, Reguilon, Hojbjerg, Winks, Sissoko, Ndombele, Alli, Lamela, Moura, Kane, Vinicius, Bale, Son.
Manchester United provisional squad: De Gea, Henderson, Grant, Lindelof, Maguire, Shaw, Telles, Tuanzebe, Wan-Bissaka, Williams, Diallo, Fernandes, Fred, James, Mata, Matic, McTominay, Pogba, Van De Beek, Cavani, Elanga, Greenwood, Rashford.