Foden, 20, and Greenwood, 18, both made their senior England debuts in the 1-0 victory over Iceland on Saturday evening.
But Icelandic outlet DV have reported that girls were invited into their room on Sunday and have revealed video footage which was posted on Snapchat.
Speaking to DV, one of the women in the Snapchat video said: ‘We had no idea about these rules, they never said we could not take pictures.’
She also claimed to have been in a relationship ‘with one of the boys for a few days’, and added: ‘The only thing I can say is that I had been talking to one of them for a few days. I’m not going to say where.’
City midfielder Foden has a two-year-old son and a long-term partner Rebecca Cooke, meanwhile United forward Greenwood broke up with his girlfriend earlier this year.
Both players did not train with England’s squad in Iceland’s capital Reykjavik on Monday.
England’s players were ordered to follow strict rules for their trip to Iceland, which included no visitors to the team’s hotel.
It’s understood that the rule regarding no visitors even includes members of a player’s family.