The Daily Mail have reported a player tested positive in the latest round of twice-weekly tests.
Last week, North End striker Jayden Stockley tested positive but it is not known who the second player is.
The EFL will only issue the latest set of tests results from the Championship on Thursday and PNE are unable to comment until then.
North End's latest tests were carried out yesterday morning (Monday) before training at Springfields - they were still training in small groups then.
Today, the club began contact training after getting permission from the EFL.
Like Stockley, the second player to test positive will have to self-isolate at home for seven days.
It is understood that none of the other North End players will have to isolate following this second test despite a return to group training.
PNE have taken advice from the EFL and followed the EFL's protocol document on positive tests.
That advice does not state that other players have to self-isolate.
The EFL's protocol is that other players should only have to self isolate if deemed by medical staff to have been in prolonged close contact - two metres for 15 minutes or more - with the player who has tested positive.