Sutton yesterday described Dembele, who scored twice against Manchester City last month and has 13 goals already this season, as the “player of the moment” in British football.
His potential was signposted with 17 goals for Championship club Fulham last season so Sutton is mystified why an English Premier League club did not take a chance with Dembele, still only 20.
“Down south I think he is the most talked about player at the moment,” said Sutton, BT Sport’s Scottish football expert. “Whether we like it or not there is going to be interest in him. Celtic will be doing their utmost to hang on to him.
“In such a short space of time looking at him he has all the attributes and I still think he’s a little bit raw around the edges and he’d admit that himself.
“But he can move in behind, he can hold the ball up, he’s a physical presence, his link-up is decent.
“He’s essentially potential at the moment, so heaven help centre-halves when he’s matured a bit. At £500,000 [he] is just an unbelievable signing.
“There are probably recruitment people down south getting their backsides kicked, saying why didn’t we take a chance on him because his stock has risen in such a short space of time. And I think he’s only going to get better.”
The former Celtic striker could not understand why top-flight English clubs, with money to spend, were not drawn to Dembele.
“He did well in the Championship last season. His partnership with [Ross] McCormack essentially kept up a really poor Fulham,” said Sutton. “Sides in the Premier League want the finished article for a striker. But people are now looking at him and seeing he is a real handful.”
Sutton likened Dembele to a former Chelsea striker. But he added that it’s Didier Drogba whom he thinks Dembele resembles rather than himself.
“At least when people played against me, they could think: ‘Oh well, he can’t run’,” said Sutton. “When you actually look at him, who would want to play against him? It’s like playing against Drogba.
“When the ball goes out wide at times, I think he can get himself more in between the goalposts like a [Henrik] Larsson type. These are small things he can improve on.”
But Sutton isn’t yet convinced Dembele could have the same impact for Celtic as Larsson. “It’s early days, isn’t it? Could Celtic hold on to him for seven years? I’m not so sure.”