ESPN revealed on Monday that the 30-year-old had become the latest high-profile player to be targeted by Saudi clubs with Al Ittihad offering the forward a four-year deal worth €30 million ($32.7m) per season.
A source close to negotiations suggested the Saudi side were preparing an opening bid of €60m ($65.4m) plus bonuses, but Tottenham indicated they were unwilling to listen to offers for the South Korea forward.
Speaking on Tuesday, Son moved to dampen speculation over a transfer by reiterating his commitment to Spurs.
Son is quoted by Korean football reporter Sungmo Lee as saying: "I have many things to do in the Premier League. Money doesn't matter to me now, and the pride of playing football, to play in my favourite league is important. I want to play more for Tottenham in the Premier League. I'll prepare well when I'm back to Spurs."
The source suggested there was some optimism Son could be tempted into a move to Al Ittihad given the club have already agreed a deal to sign France striker Karim Benzema, with Chelsea midfielder N'Golo Kante expected to follow imminently on another free transfer.
However, Son is under contract at Tottenham until 2025, and negotiating a deal would have meant overcoming Spurs' reluctance to sell.