Harmanpreet scored 66 against the UAE earlier in the tournament and now has a total of 3415 T20I runs to her name, with the 35-year-old surpassing Lanning's tally of 3405 runs with her most recent knock.
Mandhana has 3378 T20I runs to her name and could become the third highest run-scorer in the history of Women's T20I with a big score against Bangladesh in the semi-finals of the Asia Cup.
New Zealand veteran Suzie Bates remains the leading run-scorer in the history of women's T20I cricket with 4348 runs and the 36-year-old recently added a team best 117 runs during the
five-match T20I series against England.
But Harmanpreet and Mandhana have appeared to be in good touch of late and could make further inroads on the Kiwi with decent innings at the Asia Cup.
Women's Asia Cup semi-finals schedule (both to be played on July 26)
First semi-final: India v Bangladesh, Dambulla
Second semi-final: Sri Lanka v Pakistan, Dambulla.