Farrell was the man in possession of the jersey at the beginning of England's summer tour but turned to Flood to get the backline firing.
But the Saracens fly-half is happy to bide his time, and improve his game, for the greater good of the Red Rose set-up.
"I don't see it as a rivalry with Toby," said Farrell.
"There are a lot of good players in the Premiership now and a lot of good players in the squad at England.
"All you've got to do is put your best foot forward and play as well as you can each week."
The duo have both been tipped to win call-ups to the Lions squad to tour Australia next year, whole George Ford and Danny Cipriani are also in the England reckoning.
But Farrell reckons Flood is still the master at fly-half and admits he has learnt a huge amount from the Leicester Tigers man.
"I've taken a lot of things from Floody. He's been around for a while and he's not even that old, he's only 26," added Farrell.
"He's very experienced and he knows what he's doing, you take as much as you can off people like that."