If chosen, the back-row forward - who stood down from the Wales captaincy for this year's Six Nations - would become just the second man after England great Martin Johnson in 1997 and 2001 to captain the Lions on two tours.
Gatland clearly feels a different style of approach will be required to defeat New Zealand on home soil and England's loss to Ireland in Dublin did not enhance the chances of some contenders.
To celebrate The White Horse pub in London's Parsons Green becoming Thomas Pink's Pink Lion for the day, member of the British and Irish Lions squad Ben Youngs helps out with a touch rugby session during a rugby family fun day hosted by Thomas Pink, the Official Outfitters to the British and Irish Lions Australian Tour.
Gatland is likely name up to 40 players, just four fewer than Sir Clive Woodward took to New Zealand on the ill-fated 2005 trip.
Wales flanker Sam Warburton, one of the favorites to be captain for the British and Irish Lions' tour to New Zealand, has been ruled out for about six weeks because of a left knee injury.
Older brother Tom started the first two matches and came off the bench in the decider but the 30-year-old Leicester hooker has since dropped out of England contention and isn't expected to retain his place in the squad.
According to the report, England captain Dylan Hartley will miss out.
The Lions went on the thrash the Wallabies in that decider and secure Gatland's place in the team's cherished history, but there were many who believed that he was deploying a game based on battering down the opposition as he had done so similarly with Wales.
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But while Hartley will miss out, George will be included, and England will also provide the bulk of the front five, with Joe Marler, Mako Vunipola and Dan Cole ajoining Sinckler among the six props, along with Ireland's duo Jack McGrath and Tadhg Furlong.
Stuart Hogg, Leigh Halfpenny, Elliot Daly, Owen Farrell and Greig Laidlaw are all proficient goal kickers but will be under consideration for positions other than fly-half.
Joseph has been tipped by many pundits to start the Test series at outside centre, but Gatland's preference for size in the midfield could see the likes of Te'o and Wales' Jonathan Davies preferred.
"It has been a hard process".
"You play whatever role you're given", he said. You have to consider whether he would be a good tourist in other personality aspects.
Henry added of the Lions: "They are remembered by the test match results but sides gain confidence and momentum through the games they play leading into those test matches and if they don't get success in those games, confidence is not going to be high and that is going to affect the way they play in the test matches".
The problem for Gatland is that he doesn't really know who his centre pairing will be going up against.