The brothers join fellow Kiwis Steven Adams, Kirk Penney, Rob Loe and Thomas Abercrombie in having a crack in Summer League, which will be teeming with scouts.
Tai will initially play at the Orlando Summer League from July 1-6, while Corey will play solely in Las Vegas, from July 7-17.
For Corey Webster, it will be his second time with a NBA franchise, after previously attending training camp and pre-season with the New Orleans Pelicans in 2015.
After winning the New Zealand NBL MVP and championship with the undefeated Wellington Saints, Webster jetted off to a Mavericks mini-camp this month, and impressed enough to get the call to attend Summer League in Las Vegas.
Much like when he was with the Pelicans, he has been given every chance to make the NBA by the ANBL team he is contracted to. Webster is currently on the books of the Perth Wildcats, and can come back to the league if he can't crack the NBA.
Tai, meanwhile, will combine with NBA quest with the opportunity to perform in front of the many overseas teams and scouts looking on.
Many of those scouts come from European sides, with Webster's international appearances and his senior season at Nebraska - 17 points, five rebounds and four assists per game - set to be good enough for a European gig if the NBA doesn't come calling.
That decison will be made after he chases his NBA dream though. The Webster brothers' success there could also have an impact on whether they are available for the Tall Blacks' Asia Cup campaign in Lebanon in August.
When asked last month, Tall Blacks coach Paul Henare was supportive of his players giving their all to make the NBA.
"It's something that we fully support and we'll just have to wait and see," said Henare.
