And the 37-year-old – brought to St James's Park by Sam Allardyce last summer – could be confirmed as David Moyes's new No 2 early next week.
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Sports View podcast with Ian LawsThe Echo can reveal Premier League big guns Chelsea have also been looking at Round as a possible replacement for ex-United assistant manager Steve Clarke, who had his contract terminated last month after the appointment of Portugal coach Phil Scolari.
But no decisions on Scolari's backroom will be taken until the Brazilian fully takes the reins at Stamford Bridge.
Round, meanwhile, is only contracted to United until the end of the month, and Kevin Keegan is understood to have been keen to keep him at Newcastle.
However, he has not been offered a new deal, and Moyes – who has been looking for an assistant since Alan Irvine left to take charge of Preston North End midway through last season – has finally made his move for Steve McClaren's former Middlesbrough and England No 2.
Negotiations with Round's agent are expected to start over the weekend, when Everton's chief executive Keith Wyness returns from holiday.
Round's likely departure to Goodison Park will leave a vacancy on Keegan's backroom staff, and they 57-year-old will be keen to bolster his coaching team – led by former Tottenham Hotspur No 2 Chris Hughton ahead of the new campaign.
The full article contains 261 words and appears in Sunderland Echo newspaper.