Nate Diaz also keen to step into the boxing ring after Conor McGregor gets boxing licence.
Swanson is scheduled to face Doo Ho Choi at UFC 206 on 10 December.
McGregor was stripped off the featherweight title cutting short his 2-weight title reign.
White has heaped praise on Mayweather's unbeaten streak.
McGregor is confident he can beat Mayweather if they meet in the ring for a boxing match.
Nate Diaz lost his UFC 202 to Conor McGregor.
Lobov wants the fight between McGregor and Mayweather to take place.
McGregor attained a California boxing license at the end of November.
WrestleMania 33 takes place at Camping World Stadium in Orlando, Florida on 2 April 2017.
McGregor is currently taking a break from Mixed Martial Arts.
McGregor created history at UFC 205 by becoming the first fighter to hold two-weight titles simultaneously.
The Irishman had won the featherweight title after knocking out Brazilian Jose Aldo at UFC 194 almost a year back.
Dubliner has persistently teased the possibility of a fight with Floyd Mayweather.
Alvarez lost his lightweight title to McGregor at UFC 205 in New York.
Kavanagh says he would bet on a fight between McGregor and Mayweather taking place next year.
The Irish fighter has been granted a license to box in the state of California.
The 28-year-old is taking a break from UFC until after the birth of his first child.
Ferguson has won his last nine fights, which includes the win over Rafael dos Anjos in his last bout.
McGregor became the first person in the history of the UFC to hold two title belts at the same time.
Aldo has been installed as the new featherweight champion by UFC authorities.
McGregor is currently taking a break from the sport.
Mark Henry believes the Irishman needs to beat Frankie Edgar and Khabib Nurmagomedov to be called the greatest.