The Magpies’ board had released a statement saying that nobody from the club should comment in public about the situation, with the player having been transfer-listed and made available on a free after criticising the club.
But Pardew told Sky Sports News: “I’ve never closed the door on anyone and I’m not closing the door on Joey.
“He trained with the development team today and, who knows, he may train with the first-team soon.”
Barton, whose disappointment at not being offered a long-term extension to his contract has been well-publicised, jokingly hinted at building bridges immediately after.
Posting on Twitter, Barton quipped: “Does anybody have Isambard Kingdom Brunel’s number?”, referring to the famous historical builder of bridges.
Earlier, Newcastle had sought to stop the situation from playing out in the public eye.
In a statement, they said: “We understand the level of interest in the club’s decision to offer Joey Barton a free transfer.
“However, it would not be dignified, nor would it serve any useful purpose at this present time, for either the club or Joey to air their private issues on this matter in public.
“The club and the player have important business to focus on over the coming days and both parties have come to an agreement that we will not comment further at this time.”
Barton’s situation is understood to be being monitored by several Premier League clubs.
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Alan Pardew leaves door open for Joey Barton to stay at Newcastle