Praise be to Allaah.
If the situation is as described in the question, then that is permissible, because it is permissible for each of them to look at the other with the intention of enjoyment. See question no. 3801.
And it was narrated from the Prophet SAWS (peace and blessings of Allaah be upon him) that a man should cover his ‘awrah except from his wife and female slave (concubine). It was narrated that Bahz ibn Hakeem said: my father told me from my grandfather, who said: “I said, ‘O Messenger of Allaah, with regard to our ‘awrah, from whom should we cover it?’ He said, ‘Cover your ‘awrah from everyone except your wife or (the slave woman) whom your right hand possesses.’ He asked, ‘What if a man is with another man?’ He said, ‘If you can avoid letting anyone see that, then do that.’ He asked, ‘What if a man is on his own?’ He said, ‘Allaah is more deserving that he should be modest before Him.’” (Narrated by al-Tirmidhi, al-Adab, 2693; classed as hasan by al-Albaani in Saheeh Sunan al-Tirmidhi, no. 222). The hadeeth indicates that a person should cover up when he is alone. And Allaah knows best.
Sheikh Muhammed Salih Al-Munajjid