The South Korea international attacker joined Spurs from German club Bayer Leverkusen last week, subject to work permit and international clearance.
Son is a highly-rated player who can play as a winger or as a forward, but Honigstein has highlighted some flaws in the 23-year-old’s game.
“The problem is that he is a little bit flaky, little bit lightweight,” said Honigstein on the ESPN FC show on BT Sport 1 last Friday morning.
“He is a guy with huge potential, but does he have the consistency, the mental strength and character to really thrive? I am not so sure.”
Son was one of the best attackers in the Bundesliga last season, helping Bayer finish fourth in the league table.
The South Korean scored 11 goals and created 39 chances in 30 league appearances during the 2014-15 campaign.
Son had a pass accuracy of 76% and a shot accuracy of 54%, and won 30 headers, 49 dribbles and 30 tackles.
The former Hamburg star became Spurs’ fifth signing of the summer transfer window following the arrivals of Kevin Wimmer, Kieran Trippier, Toby Alderweireld and Clinton N’Jie from FC Koln, Burnley, Atletico Madrid and Lyon respectively.