You could say "She said she likes swimming." or "She said that she likes swimming." [Note the "s" on the verb like.] Using "that" is optional; I think it sounds better to include "that," but it may just be a matter of personal taste.

For stative verbs like: love, like, hate, stand, believe etc, you cannot keep the verb in present, since you are reporting something, and the action may be not the same after saying it. I like cheese. - She said she liked cheese. ( This would be true at the moment of speaking, but what if you report it 2 weeks/months/years later?)