Shot-stopper Eastwood spent time on loan at Portsmouth and Rochdale last season, adding to a lengthy period away from Bramall Lane on temporary deals.
The 25-year-old could now be set to head north of the border to Scotland with Scottish Premiership outfit Ross County.
He has headed to Ross County to link up with the club on their pre-season tour to Italy.
Eastwood is on the verge of joining the Scottish outfit and has taken a spot on the travelling party.
The 25-year-old came through the youth set-up at Sheffield United and has been out on a series of loan stints to hone his skills.
Ross County finished in sixth in the Scottish Premiership last season.
They start the new season by taking part in the Scottish League Cup, while their first Scottish Premiership game comes away at Hearts at the end of July.
