Invigilation of all external exams is the final task that will be handed over to support staff under the workforce agreement.
But some heads and teachers are worried that using external invigilators will make tests more stressful for children, reigniting concerns over formal testing of 11-year-olds.
Sid Willcocks, head of Epiphany school, Bournemouth, said: "Primary children want the reassurance of their teacher. I wouldn't wish somebody else to drift in and supervise the Sats. It is essential to have their teacher."
Angeles Walford, head of the Priory Church of England primary, Wimbledon, south London, said: "The KS2 Sats are high stakes. They are stressful for children and stressful for staff.
"Teachers have a calming influence on children and I don't think teachers would want to be out of the room. If they want to be there the head should support that, but they don't have to do it."
One contributor to the primary area of the TES website chatroom said that handing over invigilation to others could prevent Year 6 teachers being tempted to help pupils in the tests.
But others disagreed. "I think it would be quite sad not to invigilate. You work with these children all year, and then when it actually comes to sitting them that teacher is not there," said contributor "Pinktulip".
"Ronan" said: "Why can't we simply go back to the idea of teacher from school A invigilating at school B? That way pupils would have one familiar and one unfamiliar teacher in the room."
"Kailundo" added: "I would hate to not be there when the children are taking their Sats... Having an external examiner would freak them out!"
But Chris Keates, general secretary of the teachers' union NASUWT, said: "There is no evidence to demonstrate that not having a teacher present in the room will increase the stress on pupils."
She said the absence of the teacher did not mean that there would be "a stranger in the room" as support staff who worked with the children could invigilate instead. "There appears to be no end to hypothetical problems some people will apparently dream up to prevent teachers having a professional role and contract," she said.
Primary Forum 24 Join the debate on our website at www.tes.co.uk