The 24-year-old Londoner will sit out the Clydesdale Bank Premier League clash with St Mirren and looks set to miss the rest of the season after suffering a punctured lung and broken ribs in the weekend win over Ross County.
But Shiels claims the former Crystal Palace trainee has done well enough in his 31 outings this season to merit a call-up for Hodgson's squad.
He said: "We have lost Dayton which is a big loss for us. He's a big player and adds a lot in the attacking third. He was on the verge of an England call-up, we were thinking.
"I know you might find that funny but other players who have been recommended for Scotland and England are not in the same league as James.
"I don't see why, just because he is wearing a Kilmarnock shirt, he can't be recognised as an international player and I think he is on the verge of it.
"It's obvious that because he is playing for Kilmarnock, (James) wouldn't get the same recognition but believe me, he is good enough. Technically (he's good enough) and his game understanding has improved considerably since he came up here and over the last four or five months he's been one of the top players."