Current Blues skipper John Terry is widely expected to leave the defending Premier League champions in the summer when the 35-year-old’s contract expires.
Ivanovic, who moved to Stamford Bridge from Locomotiv Moscow in 2008, is one of the longest-serving players at the west London side.
The Serbia international has struggled with form throughout the campaign after the defending champions made a disappointing start to the defence of their league crown.
Former Liverpool and Tottenham Hotspur midfielder Murphy questioned whether Ivanovic would be the best man to succeed Terry in the captaincy role.
Asked if Ivanovic could captain Chelsea on a permanent basis, Murphy said: “Maybe.
“It depends on how many players that they bring in.
“Do they want more youth and athleticism in the back four because his form hasn’t been great this season.”
Ivanovic has scored one goal and has made two assists in 22 Premier League appearances so far this season.
The Serbian defender has netted 32 times in 343 appearances during his Chelsea career.
The Blues face Southampton at St Mary’s in their next Premier League game on Saturday.
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