Second-place United welcome the relegation-threatened Potters - under the management of Eddie Niedzwiecki with new boss Paul Lambert watching from the stands - to Old Trafford fresh from a warm-weather training camp in Dubai that saw the squad recharge their batteries after a busy festive schedule involving five matches in a two-week span.
Such a break allowed experienced right-back Valencia to recover from a hamstring issue suffered during the 2-1 win at West Bromwich Albion on 17 December that resulted in an absence of six matches including the FA Cup third-round defeat of Championship promotion contenders Derby County last time out.
Mourinho confirmed that the 32-year-old was now "ready to play", though Martial could miss out due to an unspecified injury sustained during a training session in the United Arab Emirates (UAE).
ESPN report that Michael Carrick is in line to make the matchday squad for only the seventh time this season after undergoing a cardiac ablation to correct an irregular heart rhythm, while second-choice goalkeeper Sergio Romero is also said to be available after missing the trip to Dubai.
"Martial is not ready, but I hope he can play," Mourinho told reporters, per United's official website. "Plus, the other ones that are unavailable [long-term absentees Eric Bailly and Zlatan Ibrahimovic]."
Martial has scored nine times in 30 appearances across all competitions for United so far this term and netted his first goal since November with a terrific strike in the 2-0 victory over Everton on New Year's Day.
The French international could yet be dragged into the ongoing Alexis Sanchez transfer saga, with the Evening Standard now reporting that Arsenal manager Arsene Wenger wants to "explore his availability" as part of a possible January part-exchange deal.
Contract rebel Sanchez was left out of the Gunners' squad for Sunday's [14 January] dramatic 2-1 loss at Bournemouth with his future expected to be clarified in the next 48 hours. United are understood to have moved ahead of Pep Guardiola's Manchester City in the race to sign the Chilean due to their apparent willingness to either pay a higher £35m ($48.1m) fee or include a player as a makeweight.
Arsenal, also reportedly on the trail of Bordeaux playmaker Malcolm and wantaway Borussia Dortmund frontman Pierre-Emerick Aubameyang, have been linked with Martial on more than one occasion in the past, while the underwhelming Henrikh Mkhitaryan could also form part of negotiations for Sanchez, who nearly reunited with former Barcelona coach Guardiola in a £60m deal on summer deadline day.
That agreement collapsed at the 11th hour due to Arsenal's failure to sign AS Monaco midfielder Thomas Lemar as a replacement.
Quizzed on Mkhitaryan's future over the weekend, Mourinho said that "every player has a price" but stated that the Armenian would probably play again against Stoke having started in the FA Cup.