The messages refer to three black players from England who did not score penalties in the final of Euro 2020 at Wembley Stadium.
England stars Marcus Rashford, Jadon Sancho and Bukayo Saka have all faced a torrent of racist abuse online after their shots at Italy on Sunday.
Portsmouth Black Lives Matter has already announced a 48-hour boycott of social media in response.
A single screenshot is widely shared on social media today and appears to be from a group Snapchat conversation.
There are references to lynchings, bombings, and death threats with monkey emojis, along with the N word.
It is unclear if this originates from an academy group chat, and the club is now investigating.
The club is understood to have notified the EFL and Kick It Out regarding the alleged discriminatory charges, but at present the club's investigation is the only one underway.
The investigation is being carried out by Portsmouth's top management and it is understood that it focuses on the single screenshot that has been widely circulated on social media, and that the club is not aware of any additional abuse within the chat.
A Pompey spokesperson said: 'The Portsmouth Football Club is aware of images circulating on social media that allegedly originate from a u18 academy group chat and are discriminatory in nature.
'The club has launched an immediate investigation and will provide an update once it is completed.
โPortsmouth Football Club strongly condemns racism and is fully committed to the elimination of all forms of discrimination.
"There is no place for it in our game or in society as a whole."
Havant and 6th division Waterlooville FC announced on Monday that they had removed a volunteer from their position after 'discriminatory' posts on social media after England's defeat.
The Pompey Supporters' Trust has said it is "shocked and dismayed" by the allegations.
A statement read: โWe appreciate the club's investigation and, following discussions with the club, we are aware of the seriousness and urgency with which this matter is being addressed.
โThe PST is fiercely opposed to all forms of discrimination and abuse. These vile and abhorrent messages have no place in football or anywhere else in society. "
