Leinster coach Cheika has revealed that Saturday's game might come just too soon for O'Driscoll, who has been sidelined since sustaining a hamstring tear against Wales in the Six Nations last month.
"I'd say Brian's chances of playing are low. We're hoping (that he'll be fit). He's training as much as he can and he's doing everything he can to get ready for the game, but I'd say his chances of playing are low," Cheika conceded.
"But we're not giving up on it yet and we're not going to risk him in any way. If we think he can play, then he will be involved at some stage."
Commenting on some of Leinster's other injured players, he added: "Gordon (D'Arcy) is going to be out for a few more weeks. We're probably going to be looking to play this weekend and next without him and then we have a weekend off, so we'll see how he is then.
"Mick Berne has an ankle problem from the Llanelli game when he had to come off, while (Christian) Warner has a back problem which is why Eoin O'Malley is in the squad.
"We need some cover in the centre and he is an out-and-out 13. I know that it'll be a big game for him to play, with it being at home, but he has had some good form in the Ireland Under-20s so we've got a lot of confidence in the young fella."
The Australian has talked up Munster ahead of this weekend's derby clash at the RDS, dubbing the southern province 'the best team in Europe' off the back of their fine Heineken Cup quarter-final win at Gloucester.
"I think that weeks like these are the most enjoyable because it's like a cup final atmosphere. Obviously there's a lot of tension that goes down when two provinces meet but there's a lot of respect between the two teams," Cheika said.
"They had a very good performance last weekend against Gloucester and dominated the game and the opposition into playing how they wanted them to, and that's why they're so good at it. That's why they're the best team in Europe.
"We've got to make sure we learn from some of the mistakes that Gloucester made, and that we don't make the same ones on Saturday."
Some observers may feel that Leinster could throw an envious glance at Munster as, after another disappointing European campaign for the men in blue, they are only in the running for league success.
Cheika was quick to dispel such a notion, adding: "Is there envy towards Munster? No, they deserve all the plaudits they get. There's a quantum shift that has to go on, and we don't worry about what goes on with Munster.
"We worry about what happens with Leinster. If they go on to win the Heineken Cup, and I think they will, then good on 'em.
"Jealousy will get you nothing. Hunger will get you everything.
"They're a very, very strong team and we're going to have to play very well to beat them. And we really want to beat them. We want to make sure that we're very well prepared for it."
Ollie Le Roux has made himself a firm favourite with the Leinster players and supporters alike during his short time with the province and as he enters his final run of games, Cheika spoke of the former Springbok prop in glowing terms.
Commenting on Le Roux, who is out of contract at the end of the season, the Leinster boss said: "I think we'll still have some contact with him (after he goes). We have a very good relationship and he has had an unbelievable effect on the squad.
"He definitely wants to keep some sort of involvement with us, so we have got some plans in terms of broadening our horizons with him.
"But he has had a great impact and hopefully he'll have as big an impact this weekend. He's up for the game and as we proceed with the competition for this season, he's determined to finish off a job well done so far.
"I'm just happy that he has done a good job for the team. The team enjoys his company. He is definitely not lacking in confidence and he has put that confidence into a lot of the players," Cheika surmised.
"He's also very giving in terms of imparting his knowledge to the younger players. Hopefully we will be able to have a continued relationship beyond this season."
Leinster are contemplating the idea of sending some of their younger players to South Africa during the off-season to gain some valuable game-time, with Le Roux earmarked as an intermediary for the scheme should it get the go-ahead.