Everton announced on Monday night that they had agreed a fee with Major League football for the midfielder who joined them from Millwall in 2004, scoring 68 goals in 278 appearances.
A statement on the club's official website said: "Everton have agreed with Major League football (MLS) that Tim Cahill can be transferred to the New York Red Bulls. Tim, 32, will move to the Red Bulls for a nominal fee, subject to agreeing personal terms and passing a medical. He will travel to the US in the next few days."
The move would come as something of a surprise although Cahill's departure could pave the way for Pienaar to re-sign for Everton, following a noteworthy loan spell from Tottenham last season.
With attacking midfielder Steven Naismith also signing from Rangers this summer, Cahill may seek new pastures to guarantee himself first-team action. He would join former Premier League players Thierry Henry and Teemu Tainio in New York, while former Barcelona defender Rafael Marquez also plies his trade at the Red Bull Arena.
Cahill, who has scored 24 goals in 55 appearances for Australia, would also come up against former team-mate Landon Donovan, who plays for Los Angeles Galaxy but has had two loan spells with David Moyes' men.
The 32-year-old would end his career at Goodison Park on a sour note after being sent off on the final day of last season against Newcastle following a clash with Toon midfielder Yohan Cabaye.
Although the Frenchman apologised for his comments on Newcastle's official website, Cahill was still handed a three-match ban after Everton's appeal to the Football Association was rejected.
And while he accepted the suspension, he was left "disgusted" by Cabaye's comments, adding: "I don't wish to elaborate on the exact detail of what was said - but his words have no place either on or off the football pitch.
"Cabaye has apologised via his club's website and as far as I am concerned the matter is now closed."