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The Crusaders coach revealed in August after missing out on the All Blacks job to Ian Foster, he approached Gatland about joining the team in their tour of South Africa in 2021, with a desire to fill out his CV with international coaching experience.
Robertson says he's in ongoing talks with Lions management, which have been promising.
"We've had some good conversations the last couple of weeks around the opportunity. I'm looking at potentially being involved with the team, that could play against the Springboks and then stay on in some capacity.
"It wasn't an assistant role I was wanting it was a learning opportunity for me, [to] help a lot around the professional development and support their current coaching group, it wasn't about being an assistant as such.
"Those conversations are continuing … it's a highly likely chance, I'm finding ways I can get there."
Any involvement will follow on from the 46-year-old's duties in Super Rugby, where he will look to win a fifth consecutive title with the Canterbury franchise in next year.
Robertson earlier revealed he had aspirations to coach oversees, and recognised the sensitive timing around roles on the international market. He played in France for three years to learn French, in the hope of boosting his chances to coach there one day.
The Lions series in South Africa kicks-off on July 3, with the three tests running on three consecutive weekends from July 24.
Meanwhile, Robertson has this morning revealed his squad for next year's Super Rugby Aotearoa campaign, and will need to utilise the depth within his squad right off the bat.
All Black Braydon Ennor is out for the entire season with an ACL injury, while fellow international George Bridge along with Manasa Mataele with miss the start of the season, both with pectoral injuries.
That will see the likes of Leicester Fainga'anuku and Dallas McLeod relied on more in the first team, players Robertson has touted as having big seasons in 2021.
"We've got a lot of guys that can play in multiple positions.
"Leicester during Mitre 10 Cup was carrying a few people out the on the field, he's an awesome talent. If you want to win championships you need depth and if George is out, Leicester comes in. There's great completion in all positions."