Round is on the England coaching staff with his former Boro boss Steve McClaren, and he is likely to continue with this role.
England Man Joins Allardyce
Round, 36, had his playing career cut short by injury but joined the coaching staff at Derby, before joining McClaren at the Riverside.
The Magpies are hoping Round will be able to join them next week in Austria for their seven-day training camp.
This puts a question mark over the position of Nigel Pearson, although according to the Chronicle: "the ex-Carlisle boss is under no pressure to quit St James' Park, along with last season's reserve-team coach Lee Clark and Terry McDermott".