The 36-year-old Cardiff Blues loose-head prop missed the 2017 Six Nations campaign after having surgery on a ruptured bicep.
Jenkins captained Wales in three of their four 2016 autumn internationals before suffering the injury.
"It was bad timing," he said. "I've definitely got the hunger to get back that starting spot."
He added: "I was happy with how I performed and the honour of being captain."
Rob Evans was preferred for Wales in the 2016 Six Nations, but Jenkins, who has 129 caps, reclaimed the jersey when the Scarlets player was injured - only for the bicep injury to strike.
Now, with the British and Irish Lions tour of New Zealand and Wales facing Tests against Samoa and Tonga on their summer tour, it may be a busy summer for Jenkins.
He toured New Zealand with the 2005 Lions and went again in South Africa in 2009, making five Test appearances, but injury meant Jenkins was forced off the 2013 trip to Australia.
Jenkins would not be drawn on any hopes he has of going to New Zealand again in 2017 with the Lions.
He says he "wouldn't turn down the chance" to add to his 129 Wales caps if the call comes, however.
Jenkins' immediate focus is Blues' Judgement Day game against Ospreys at Principality Stadium in the Pro12 on Saturday, 15 April.
Since returning from the bicep injury, he played the full 80 minutes of their European Challenge Cup defeat by Gloucester and 76 more in Friday's 24-24 draw at Ulster.
"I am concentrating on getting fitness under my belt," said Jenkins.
"If in four games time I'm back to where I hope I am, I wouldn't turn down the chance to play [for Wales]."
Jenkins is up for the challenge posed by Evans and Ospreys' loose-head Nicky Smith.
"To come from being captain to being injured for three months makes you experience the highs and lows," said Jenkins.
"There's obviously a progression plan with the boys coming through, but I'll always have the drive to win back that number one jersey."
Wales' most-capped player Gethin Jenkins says he is "hungry for more caps" after a long injury lay-off.