Remy scored the opening goal in Tuesday night's 6-0 Champions League Group G win over Maribor before departing with a groin injury which saw Mourinho rule him out of the United duel.
Chelsea's first team had a day off on Wednesday, with Mourinho insisting he did not wish to know any injury news until preparations for Old Trafford began in earnest on Thursday.
Remy is hopeful of playing in what would be a boost for the Portuguese.
The France striker said: "I will see what happens in the next few days
But I am ready for Manchester United, of course.
"I got the injury before I scored
I felt a little bit sore
I preferred to keep going and stay on the pitch
I really hope that it is not too bad.
"These things happen but the most important thing is we won
I was disappointed when I came off but there is no reason to be afraid.
"We must now look forward to the game against Manchester United."
Remy was deputising for Diego Costa, the scorer of nine goals in seven Premier League games who is yet to feature since the international break when, Mourinho says, a hamstring problem was exacerbated on Spain duty.
Mourinho has put no timescale on Costa's return, only saying the Â£32million signing from Atletico Madrid had "very little" chance of playing at United, but it would not be a surprise were the Blues to be headed by the formidable frontman at Old Trafford.
Costa's hamstrings have been a regular discussion point this season but, following the defeat of Arsenal - admittedly prior to Spain's matches with Slovakia and Luxembourg - captain John Terry questioned where the reports of an injury had come from and described his team-mate as a handful in training.
Mourinho deployed, out of choice rather than necessity, Andre Schurrle as a 'false nine' at United last season and, if Costa and Remy are out, will have only one recognised striker to call on in Didier Drogba.
The 36-year-old has only just returned from an ankle problem and scored the first goal of his second Blues spell from the penalty spot against Maribor.
Mourinho had declared on Monday that Drogba was not fit to play for 90 minutes, but after featuring for 75 the Ivory Coast striker was content.
"I'm happy with the minutes I played against Maribor," Drogba said.
"There was no reaction (for his ankle) so I'm happy.
"It was special to score for Chelsea again in my stadium
I always felt lucky when I had the chance to score here, to have that feeling again is great.
"It's a big coincidence scoring my first goal with a penalty after my last for the club was also a penalty in the (2012) Champions League final."
On Sunday's match, Drogba added: "It is up to the manager to decide."
Remy wanted to take his chance in Costa's absence.
"It's frustrating, of course, because I had a chance to play because Costa is injured but I am not afraid," Remy added.
"I don't think it is really bad
We will check and I really hope to play again this weekend.
"It is a huge game but every game is tough
Especially this one because it is a big game against a good opponent but I will try to recover as quickly as possible."
Mourinho gave Dominic Solanke his Chelsea debut, aged 17 years and 37 days to make him Chelsea's youngest Champions League player.
The teenager had been poised to come on at Crystal Palace but a late goal meant Drogba was sent on for stoppage time.
Solanke told Chelsea TV: "I nearly made it the other day (at Selhurst Park)
This was a lot more special at Stamford Bridge in the Champions League.
"It's a great bit of history
It's amazing, really
I'm just speechless."
As for the possibility of playing at United on Sunday, Solanke added: "You have to be ready
You've got to take your opportunity when you get it."
Source : PA