The 44-year-old is a boyhood Latics fan, but has endured a poor start to his managerial career with the club, winning just one of the seven games for which he was in charge.
Scholes took over from the sacked Frankie Bunn at Oldham after being cleared by the English Football League which decided that his 10 percent stake in fifth-tier Salford City would not represent a conflict of interest.
"He's invited here if he wants to come and have a little chat about it".
Oldham are 14th in League Two having lost three of their past five games under Scholes.
It has been revealed that the message was sent to chairman Abdallah Lemsagam on Wednesday and the message took him by surprise.
Solskjaer and Scholes played together for 11 years at Old Trafford and United's caretaker manager - who has already been in contact with his former team-mate - said he would be happy for the former England midfielder to come to see him and talk through his situation.
A statement released by Scholes after he made his decision yesterday said: "It is with great regret that I have chose to leave the club with immediate effect". I personally was always supportive of any decisions Paul made or consulted me on, reassuring him that he was the man in charge. He gave no opportunity to address any issues at all, simply resigning by text and then refusing to discuss matters.
The United caretaker manager also revealed that he is looking forward to the global break, mainly when it comes to getting some rest and relaxation.
"Players that have been injured need to train hard because April and May will be important".
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