The Auld Enemy game was once one of the highlights of the season, but since 1989 when the annual meetings ended, the two have met only four times — the last 15 months ago when England won 3-2 at Wembley.
Their last meeting in Scotland was 15 years ago when England won the first leg of a Euro 2000 playoff 2-0 at Hampden Park.
Asked if there can be such thing as a “friendly” between England and Scotland, Hodgson told a news conference: “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,” he said.
The rivalry between the two neighbours dates back 142 years to their first official meeting in 1872 with England winning 46 times and Scotland 41 since then.
Both go into the match in good spirits after Scotland beat Ireland 1-0 in their Euro 2016 qualifier on Friday and England beat Slovenia 3-1 at Wembley on Saturday.
Hodgson will definitely make one change to his starting line-up. Having allowed goalkeeper Joe Hart to be released from the squad, former Celtic keeper Fraser Forster looks set to win his third cap back on his old home ground.
“The major focus here is on Fraser Forster and if I choose him it won’t be for any sentimental reasons at Celtic Park, it will be because he deserves a start,” Hodgson said.
England skipper Wayne Rooney said he was excited about returning to Celtic where he has played for Manchester United in the Champions League.
“To play here was a completely different thing. The atmosphere before the start of the game is incredible. The fans are going to get right behind the Scotland players, and we have to be ready for it.”
(Reporting by Mike Collett in London; editing by Justin Palmer)