Murray will meet his 21-year-old compatriot Kyle Edmund, who upset Spanish world number 18 Roberto Bautista Agut 6-4 4-6 6-4, in the last eight on Friday.
"(On) the day of the match, it's always a little bit uncomfortable," Murray, a three-times grand slam winner, told reporters about facing his Davis Cup team mate.
"Normally when you see your friends and stuff in the locker room, you have a chat, joke around a bit. But on match days, it always tends to be a little bit more serious."
The 34-year-old Ferrer, who reached the China Open final in 2010 maintained his perfect career record over Fognini.
The Spaniard, bidding to reach his first final of the year, will next face in-form 19-year-old Alexander Zverev, who beat American Jack Sock 6-4 6-2 to reach the quarter-finals.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
