He told me that he swims every day.

If it is a reported speech, then the first one is correct. He told me that he swam everyday. :)

Depending on context, both can be correct. More information: https://www.ef.com/ca/english-resources/english-grammar/tense-changes-when-using-reported-speech/ [excerpt] You do not need to change the tense ... if the original statement was about something that is still true,

He swims every day

If it is a reported speech, then the first one is correct. He told me that he swam everyday. :)