BOSTON (AP) _ The mother of a 10-month-old boy who received a new liver after a tense wait that attracted the attention of President Reagan said Sunday she was grateful to the donor family and optimistic about her son's chances of thriving.

''I'm still nervous, but I feel very encouraged,'' said Kelly Jodoin, of Clinton. ''He looks fairly well considering what he's gone through.''

Her son, Philip, underwent 12 hours of surgery Saturday at Children's Hospital after a team of physicians brought back the liver from Georgia.

Doctors told Mrs. Jodoin and her husband, Philip, that blood is flowing through the child's transplanted liver but it may be a couple of days before it is clear if the organ will function properly.

The infant remained in critical condition Sunday, Mrs. Jodoin said.

The parents do not know the identity of the Georgia family who offered the organ.

''I feel bad for them that they had to lose their child,'' Mrs. Jodoin said. ''I just really appreciate them for being so unselfish and thinking of someone else at a time like that.''

Her son was diagnosed as having biliary atresia, a liver disease that would be fatal without a transplant.

The Jodoins admitted their son to Children's Hospital on Sept. 10. During their wait, they received a letter from Reagan urging them not to give up hope.

''Americans are a generous people and will give the gift of life once they are aware of the needs of others such as Philip,'' Reagan wrote.