No decision on Barker's future at MK Dons yet
Barker took caretaker charge of the side between Karl Robinson's departure in October and Neilson's appointment, taking charge of his final game on Saturday against Charlton.
Neilson has been joined by Hearts assistant Stevie Crawford in moving to Stadium MK, leaving Barker on the outskirts.
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Hide AdOn Saturday, Barker admitted he didn't know where his future would lie, and Neilson said it was a discussion the pair would need to have, echoed by chairman Pete Winkelman.
"It's a decision we'll make, and we haven't made a final decision yet," said Neilson.
"There's always transition when a new manager comes in, it's not something to speak about now, but we'll have those discussion in the next few days.
Winkelman added: "We have to do something that makes all parties comfortable. People have to decide what their focus and ambition is. We'll work it out over the next few days.
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Hide Ad"We're under no pressure to do it immediately. Sometimes you need to take stock and enjoy the adventure, and I think Richie has in the last few weeks."