Kiwi Gatland said "half a dozen players are in contention" to lead the squad, which will be named on 19 April.
"The captaincy is a great honour, but whoever the captain is there'll be no guarantee he plays," said Gatland.
However, one of his Lions predecessors, Sir Clive Woodward, believes the captain must be a "certain pick".
"You need one person who is going to be in the Test team without a shadow of a doubt - a Brian O'Driscoll, a Martin Johnson, a Lawrence Dallaglio type of figure," Woodward said on BBC Radio 5 live's Sportsweek programme.
Woodward, whose Lions side were beaten 3-0 on the previous tour visit to New Zealand in 2005, highlighted Wales flanker Sam Warburton as a stand-out candidate with the Welshman still the youngest captain in British and Irish Lions history after he was chosen by Gatland in 2013.
"Personally I have always been a huge fan of Sam Warburton," Woodward continued.
"He knows Warren well, he's been a successful Lions captain already. Would he be in the starting team? Absolutely, the first name on the sheet."
But Gatland reinforced that his squad decisions will come down to form and he refused to be drawn on suggestions of Warburton being given the role for a second time.
"The captain's form has to be good enough," he said on Sportsweek. "I think whoever that person is has to rise to that, the message to that person is it's a great honour to captain the Lions but your form has to be good enough to be selected for the Tests."
On Warburton he added: "He's a different captain to some other players. He leads by example. He doesn't say a lot but he has that experience.
"He's one of the guys in contention, definitely. In my mind there's probably half a dozen people in contention."
3 June - v Provincial union team (Toll Stadium, Whangarei)
7 June - v Blues (Eden Park, Auckland)
10 June - v Crusaders (AMI Stadium, Christchurch)
13 June - v Highlanders (Forsyth Barr Stadium, Dunedin)
17 June - v Maori (International Stadium, Rotorua)
20 June -  v Chiefs (Waikato Stadium, Hamilton)
24 June - v New Zealand (First Test, Eden Park, Auckland)
27 June - v Hurricanes (Westpac Stadium, Wellington)
1 July - v New Zealand (Second Test, Westpac Stadium, Wellington)
8 July - v New Zealand (Third Test, Eden Park, Auckland)
The British and Irish Lions captain will not be assured of a starting place on this summer's tour of New Zealand, says head coach Warren Gatland.