The club captain is available from Spurs this summer.
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And The Sun says MLS club LAFC are willing to pay £15m to ferry Son to the USA.
However, Spurs management are reluctant to sell Son before their preseason tour of Asia concludes.
The Europa League winners face Newcastle in Seoul, South Korea on August 3. That comes after a clash with north London rivals Arsenal in Hong Kong.
And driving ticket sales is Son, 33, who is an icon in the Far East.
As such, no decision over the South Korea attacker's future will be made until the Spurs squad are back in London.
