Fans of Mark Hamill and The Witcher video games, such as Cavill himself, will be familiar with Vesemir, as he not only trained Geralt, but serves as his partner in hunting down monsters.
Hamill is a prolific actor best known for playing two very different characters: the Joker in a number of animated Batman adaptations and Luke Skywalker in Star Wars all the way from 1977 to the sequel trilogy that finished this year with Star Wars: The Rise of Skywalker. He's had a great number of other roles both on the screen and as a voice actor, but has been in the news just as much lately for his sense of humor and heart-warming remembrance of the late Carrie Fisher. More recently, he's been connected to The Witcher as a fan-casting for season 2.
Two different artists on Instagram have provided their own interpretations of what Hamill might look like in Vesemir's boots, Bosslogic and Spdrmnkyxxiii. On Twitter, IGN quotes Hamill as saying, "I have no idea what this is or what it's about but agree it could/should be played by me." Hamill added that he still does not know who or what Vesmir is, but that Netflix should call his agent. See the fan art below.
It's not clear exactly how Vesmir will be written as the series is being adapted from the books, with influence from the video games, and some key input from The Witcher actors like Cavill, the writers, and showrunner Lauren S. Hissrich. Still, it's pretty much a guarantee that he will be grey-haired and some degree of scruffy or scraggly, as is the trend with Witchers. Hamill is no stranger to playing scruffy, grey haired mentor figures who fight with swords.
Whether Hamill will get the role or not is up to the The Witcher's producers and Netflix, but it would be fantastic to see it happen. Cavill fell in love with the role of Geralt from being exposed to the character in the video games and still had to audition for the role, but Hamill has no clue about Vesmir and is still showing interest in it. The Witcher season 2 may be as far away as some time in 2021, but has already been confirmed by Netflix, so there's a great deal that could happen between now and then.
Source: Bosslogic, Spdrmnkyxxiii/Instagram, Mark Hamill/Twitter