It is unlikely.
While there is a chance that saliva could contain HI Virus, it is unlikely that there is enough volume to result in a transmission.
The only caution I will give to this is that if one of the partners has wounds in the mouth or is bleeding then that increases the volume of virus and increases the chance of transmission.
Having said that I need to caution that there are infections that can be transmitted via saliva like Herpes so kissing is not completely risk free!
Hey, kissing doesnt transmit HIV. HIV is transmitted through sexual intercourse, contact with infected blood if one has an open wound, through breastfeeding if the mother is HIV positive and is not taking or adhering to HIV medication.