Both were substituted during Real's 3-1 victory over Malaga in La Liga on Saturday and tests are being carried out to establish the extent of their injuries.
Bale appeared to hurt his calf and Modric his knee, and at the very least they are both likely to miss Wednesday's crunch Champions League quarter-final tie with city rivals Atletico Madrid with the contest tied at 0-0 from the first leg.
Karim Benzema also missed the Malaga match with a knee problem but the club are more optimistic that he will be ready to face Atletico.
"At the moment we can't say anything but we will evaluate the situation over the next few days," Ancelotti told a news conference.
"I think that he (Benzema) will be okay (to face Atletico) as he is improving. We have several days and he could well recover."
Real trail Barcelona by two points in La Liga with six matches still to be played and the loss of Modric as they looked to make up ground is particularly damaging.
The Croatian has become a fundamental player linking the midfield with attack with his quick thinking and clever passes.
Bale, meanwhile, has struggled for form in his second season at the club.
He scored crucial goals as Real won the Champions League and King's Cup and there were high hopes that he would build on those strong performances. But instead he has faced criticism over being too selfish on the ball.
Bale remains a key player but Real do have more options in attack where James Rodriguez, Isco or the fit-again Jese Rodriguez could all play.
Ancelotti has preferred to field a regular side rather than rotating players and now coming into the final stage of the season there are signs of fatigue that some feel could have contributed to the injuries.
The pressure is already on the Italian over the manner that Real lost their way after Christmas and with the high expectations at the Bernabeu it would be difficult to accept failure to win either La Liga, the King's Cup or the Champions League.
(Editing by Sudipto Ganguly)
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