Medical and playing facilities are under review there.
Teufaiva Stadium in Nukuʻalofa is being rebuilt for the 2019 Pacific Games and WRU chairman Gareth Davies says the work may not be completed in time for Wales visit.
If the stadium does not meet criteria, Tonga will play Wales in New Zealand.
Samoa are also scheduled to host Wales on Saturday, 24 June.
"There's a Welsh Rugby Union representation out there now (Tonga) looking at a stadium that's not complete yet, so that is a difficult scenario," said Davies.
A World Rugby spokesman said they are also "involved in that site visit".
He added: "As regards the venue redevelopment, World Rugby is not contributing to the funding of that ground construction.
"We are, however, assisting the Pacific unions in funding these fixtures with Wales as we have done previously with Italy, Scotland and other teams that have toured there - and will continue to do.
"In October, our chief medical officer Dr Martin Raftery was in Tonga to look at medical facilities as part of a union review."
Former Wales fly-half Davies hopes caretaker coach Robin McBryde will be able to go to Tonga.
"It would be a good statement, a very supportive statement from Wales if we can go to both Tonga and Samoa," said the former Wales and British Lions fly-half.
"However, we're all conscious of player welfare and need to make sure all the appropriate medical back-up and, indeed, the playing facilities, are in place.
"We've had confirmation through World Rugby that medically we should be okay and the various assessments have been made in recent weeks.".
Tonga completed a first unbeaten northern hemisphere tour in their history in November, 2016.
After beating the United States and Spain, they shocked Italy 19-17 a week after the Azzurri had beating South Africa for the first time.
Photo: Tonga celebrate beating Italy in November, 2016