Rodgers' Foxes face City at the Etihad Stadium on Monday night, with the champions needing a win to ensure they go into the final day of the season in pole position to retain their crown.
Liverpool ensured that the title race will go down the final weekend as they survived being twice pegged back by Newcastle to earn a hard-fought 3-2 win at St James’ Park on Saturday .
And the full-back says he doesn’t know whether he will keep abreast of City’s Monday-night outing, but that, as a Celtic fan, he will be looking for former Hoops boss Rodgers to do his team a favour.
"I don't know [if I will watch it]," the Scot told Liverpool’s website. "I've not shied away from the other ones, it's not worked, so maybe I'll try something different!
"Look, if I watch it or don't watch it, it's not going to make a difference. I'm a Celtic fan, Brendan's left us so he maybe owes me one!
"Leicester City are a good team but Manchester City are unbelievable, they've had eight days to recover from a heavy schedule, so we are expecting City to get off to a good start so hopefully Leicester can hold on.
"We won't expect anything but all we can do is take it down to the last game. We've done that so we'll look forward to next Sunday.”
Liverpool looked like their title challenge was finally about to run out of steam at Newcastle, as they twice threw away leads given to them by goals from Virgil van Dijk and Mohamed Salah and were starring down the barrel of a costly draw.
Substitute Divock Origi, on as a replacement for the injured Salah, headed the winner four minutes from time to put Liverpool, temporarily at least, back on top of the league.
"That's us down to a tee this season," Robertson added. "How many times have we done it?
"How many times have we been written off and people think 'OK, this isn't going to be our game' or whatever?
"We just keep on coming back and we keep on scoring goals. I can't explain it. But if we don't do it next Sunday and City are crowned champions, we can be proud of what we've done, everyone.
"So we are in there, we've stuck together and hopefully we get 97 points."