Frank Warren's two big summer fights could produce a third domestic showdown later in 2011.
The promoter hasn't ruled out
Burns and Cook meet for the WBO super-featherweight title in Liverpool on July 16.
And a week earlier Mitchell and Murray clash at lightweight in London.
The winners - or losers - could find themselves sharing a ring, although there would have to be negotiations on weight.
"We've got some cracking fighters between super-featherweight and lightweight," said Warren.
"We could definitely do something at catchweight."
Mitchell and Burns were due to meet at super-feather a couple of years ago, while a showdown between Mitchell and Cook would prove to be a real local derby, with the pair of them boasting end east roots.