Office of Grand Ayatollah Khamenei (may Allah grant him long life):
If it is without seeking pleasure and the two sides do not engage in emotional talks and it does not entail any evil either, there would be no problem in it by itself; otherwise, it is not permissible.
Office of Grand Ayatollah Makarem Shirazi (may Allah grant him long life):
If the two sides meet each other within the Shari'ah rules and there is also a third person present or it is possible that a third person may enter without their permission and the two sides exchange ordinary talks, there would be no problem. If the two sides talk with the intention of marrying each other, there would be no problem in their talks to the extent necessary for marriage purpose, albeit with the observance of all Shari'ah rules and conditions.
Office of Grand Ayatollah Saafi Gulpaigani (may Allah grant him long life):
We have no information about the personal case. Generally speaking, any kind of relationship with a non-mahram that involves looking is not permissible, although it may not be with lust.
For further information, see the following indexes:
1. "Relations with a non-Mahram before Marriage"; question 1407 (site:1427)
2. "The Effects of Looking at a Non-mahram with the Intention of Pleasure", question 11469 (site: 11418).