But the young winger accepts the best way to achieve his international goal is to remain focused on his club form with London side Harlequins.
The race to secure the nationality of the Treviso-born back was thrown into sharp focus last season when his tries against Bristol and Exeter helped Quins secure a remarkable Premiership title.
Lynagh is eligible to represent the Wallabies, Italy or England, who he's played for at age-group level having spent most of his life in the country.
Even though the 21-year-old has been included in several of coach Eddie Jones' squads, he is yet to earn an international debut but was listed as a travelling reserve for the trip to France at the end of last month's Six Nations campaign.
"Greater things like England and international honours will come only if I play well for Harlequins," Lynagh said ahead of Sunday's visit to Top14 leaders Montpellier in the Champions Cup.
"It was a great experience being able to go to Paris and experience that last game with France.
"The atmosphere in the Stade de France was amazing. It is something I will cherish for the rest of my life, my first Six Nations game being able to experience that.
"But the most important thing is if I translate what I have learned in England camps to playing for Harlequins and playing well. That is all I can do.
"I would love to play for England and if I get that opportunity and Eddie calls me tomorrow and says, 'play for us' then there is no way I'm saying no!
"Really though, it's just about focusing on this weekend against Montpellier and then the following weekend and finishing off the season strongly."
Lynagh first received England recognition when he trained with the squad in September before he was in and around the group for the autumn internationals.
A bout of COVID-19 in March disrupted his time under the watchful eye of Jones but the 11-try wing is happy with the advice he has received, especially with a summer series away to Australia on the horizon.
"Eddie and myself have a really positive relationship and there is a lot of honesty going on when we do have chats," Lynagh added.
"Overall, I wasn't even selected in the initial Six Nations group, so to be able to see that progress of getting back into the squad, training there, coming back to play for Quins, then doing well enough to be invited back and go as a travelling reserve to France, I am taking the right steps.
"I have got a really good relationship with Eddie and we have had some really good chats about how I can take my game forward, where he sees me in the future and how it can align with Quins.
"But he has said the most important thing to focus on is playing as much as possible and playing well because the rest will take care of itself.
"That is something my dad has always said to me, as well as saying there is no point worrying about relationships with international coaches until you play well enough to warrant a place there."
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