Nick Compton hopes to be Middlesex captain when Adam Voges is away with Australia, despite having only rejoined from Somerset this winter.
Managing director Angus Fraser is seeking to replace Voges, who departs for international duty in mid-May.
"I have spoken to Gus and it is something I would like to do in my career before I call it a day," Compton, 31, told BBC London.
Fraser said: "There are a number who want it or are capable of doing it."
Voges agreed to join Middlesex as their overseas player for the 2015 campaign in November, replacing Chris Rogers, and was appointed Championship captain.
However, the 35-year-old was handed a Test call-up after impressing for Western Australia over the winter - being voted the Sheffield Shield Player of the Year, having made 1,358 runs at an average of 104.46.
He will play in Middlesex's first four County Championship games before linking up with Australia for a two-Test series in the West Indies and then the Ashes series in England this summer.
Compton rejoined Middlesex from Somerset in December and is eager to take on more responsibility.
|Played for Middlesex between 2001 and 2009 and re-joined the club on a three-year deal in December|
|The grandson of England great Denis Compton, he has scored 9,163 first-class runs at an average of 43.84 - including 22 centuries|
|Has played nine Tests for England but has not been selected since the 2013 home series against New Zealand|
"I think leadership is a very important part of any club," he said.
"As players you like to get used to your captain, his ideas and the way you formulate your plans.
"I've had some successful years in county cricket. It is a job I would like to learn and get better at."
However, Fraser says he is not short of options and will bide his time before making a decision.
"James Franklin captains Wellington, Dawid Malan has captained the side in pre-season, there's Compo and Eoin Morgan comes back as well," Fraser told BBC London 94.9.
"Obviously there is the potential for an overseas player to do it.
"I think we might leave it a little bit and see how things work out in the first few weeks before deciding who is going to captain the side when Adam goes."
Meanwhile, Middlesex are closing in on announcing an overseas signing to replace Voges.
"It is a bit of blow for us as Adam is a good player and a well-respected captain," Fraser said.
"Trying to find someone who is available for the whole year is very hard.
"We have identified the player we want and we are in conversation with him. Hopefully in the next two or three days we will have good news on that front."
Middlesex start the County Championship season at home to Nottinghamshire on Sunday.