Clashes between the neighbouring nations are often fiercely contested affairs, with England claiming a 3-2 victory when they last met at Wembley in August 2013.
But asked whether there was ever such thing as a 'friendly' against Scotland, Hodgson said: "Why not? I don't really know why not? The game at Wembley last year was fantastic for us, we had to pull out all the stops.
"For me that's the type of friendly you want.
"Qualifying has to be our be-all and end-all, but in between we are trying to find fixtures that will test us, give us a flavour of matches to come.
"I won't go down the obvious route of 'we don't like the Scots' or 'they don't like us' because in my lifetime it's not something I've come across.
"I don't expect it to be especially physical. It will be hard-fought I'm sure, competitive. I'm sure each challenge will be competed for, but Scotland aren't that type of team and set their stall out to play football like we do."
Captain Wayne Rooney added: "We are on a good run at the moment and I think it's important we continue this form and getting the results because we know our next game is in March and it will be disappointing if we come off a bad result with such a long wait."
