A whole host of combinations have been tried since Greenwood moved to the commentary box but England have yet to find someone who can unlock top-quality defences on a regular basis.
"I'm sure I could fill that role. It's obviously up to the coaches to decide what they want but I do feel I can give England both options," said South African-born Barritt, who has been cruelly labelled a one-dimensional hit-up merchant by his detractors.
"I'd like to think that I can adapt my role to any given game plan. At Sarries I'm very happy to do whatever the team requires.
"I played a lot more in South Africa as a 10 and a ball player but I'm happy to fulfil whatever role is required if it contributes to success."
Barritt was a central figure in stopping Biarritz from leaving London with a Heineken Cup win on Sunday afternoon as he celebrated his England call up with another solid showing for Sarries.
The 25-year-old has had to wait for his England chance after being overlooked by Martin Johnson but his painful rejections have made him even more determined to shine.
"It's been a huge week for me. It was really exciting news with the call up earlier in the week. I'm truly honoured and it will be a huge day in my life if I'm to pull on an England shirt in the Six Nations," added Barritt.
"Missing out before does make you want it more. During that time I've just wanted to keep my head down and do well for Saracens - that's what's contributed to me getting in the Six Nations squad.
"If I can put in another big performance for Saracens on Sunday and get a chance for England I'd love to take that opportunity with both hands."