Sky Sports News relayed Spurs' decision, as they seek to have the South Korean available for Sunday's final game of the Premier League season against Everton:
According to Rob Guest of Football.London, Tottenham believe Son was provoked during his clash with Jefferson Lerma.
"Spurs are hopeful that the decision will be overturned, and they believe that the dismissal was excessive punishment," said Guest. "The player will be available to face the Toffees on Sunday if the appeal to the sending off is successful."
Son reacted to a challenge from the Cherries midfielder angrily, shoving him to the floor in front of referee Craig Pawson.
The manner of the dismissal means that Son will serve a three-game ban if the appeal is unsuccessful, starting with the match against the Toffees and then the first two games of the 2019-20 season.
Football journalist Seb Stafford-Bloor thinks Lerma was fortunate to escape punishment for his role in Son's dismissal:
The match was frustrating for Spurs, as their players lost discipline. After Son's red, Juan Foyth was dismissed early in the second half for a reckless tackle, leaving them with just nine men on the field. Nathan Ake eventually netted late on to give the Cherries a 1-0 win.
Son was recently suspended for Tottenham's semi-final first leg showdown with Ajax in the UEFA Champions League, which the team lost 1-0. The South Korean, who has scored 20 goals in all competitions for Spurs this season, is set to be back in the side for Wednesday's second leg.