Giteau is currently sidelined following surgery on his troublesome right knee and is not due back in training until mid-June at the earliest.
That leaves a gaping hole at inside centre in the Wallaby midfield and there has been intense speculation as to who could replace him.
One option would be for outside centre Stirling Mortlock to move inside to take the number 12 jersey and play Tuqiri alongside him.
And the former rugby league star, who played some games at outside centre in Australia's northern hemisphere tour last year, would have no problems filling the vacancy.
"If they want to put me there, I'll be glad to play with the number 13 jersey on," said Tuqiri in the Daily Telegraph.
"It's certainly different from the wing and something you have to get used to.
"I tried to do that at the end of last year on the European tour without a lot of luck on the field but I thought I didn't go too bad."
Tuqiri agreed outside centre was one of the toughest positions to play as it requires good defensive abilities as well as foresight in attack.
Tuqiri still classes the wing as his favourite position and Mortlock has stated his preferred spot is outside centre, so an alternative plan would see the versatile Mat Rogers come in at inside centre and leave Mortlock at number 13.
Rogers played inside centre in training on Wednesday, but coach John Connolly was giving nothing away when asked who will start in that position.
"Let's just say, there is a lot of discussion who should play 12," he said.
The first Test against England is in Brisbane on June 11, with the second Test being played in Melbourne on June 17.