The Canada international appears keen to leave Goodison Park over the summer after rejecting a new contract.
Radzinski has spurned the offer of a three-year deal he was demanding and has also had a transfer request turned down by Moyes.
The 30-year-old has been linked with a move to Charlton Athletic and he only has 12 months remaining on his present contract.
Last week, he appeared to antagonise Toffees boss Moyes even further by claiming England ace Wayne Rooney should quit the Merseyside outfit.
Radzinski met with Moyes for the first time since making his comments on Tuesday morning after arriving at the club's Austrian training camp on Monday evening.
Everton's assistant manager Alan Irvine confirmed the pair have discussed the incident but declined to divulge details of the meeting.
"David had a word with Tomasz privately this morning at our hotel," said Irvine.
"Obviously he was here too late last night to have a chat and the matter will now be dealt with internally."
Meanwhile, Everton are using their training camp in Austria to assess the ability of Sturm Graz centre half Eddy Bosnar.
The stopper is believed to be available on a free transfer and Irvine confirmed the club are keen to look at the player.
‚Ç£This is an opportunity for us to have a look at the player,‚Ç¥ said Irvine. ‚Ç£He is still contracted to Sturm Graz but we have been given permission to look at him.
‚Ç£He is a big tall centre half and a bit ahead of our lads in terms of his fitness because Sturm Graz returned to training earlier than us.‚Ç¥
