Nicholas was speaking prior to Roma’s second-leg clash against Shakhtar Donetsk in the last-16 of Champions League.
He shared his admiration for the Bosnia and Herzegovina international and believes he should have been made an Arsenal player years ago.
“I love Dzeko,” Nicholas told Sky Sports.
“I always thought Arsenal should have got him.”
Roma went into last night’s second leg 2-1 down from the first leg in Ukraine.
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Arsenal players train ahead of AC Milan clash
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Nicholas predicted the Serie A side would come out 1-0 winners with Dzeko netting the only goal.
The Scot called it right as Dzeko’s second-half strike was enough to book a quarter-final spot for Eusebio Di Francesco’s side.
Dzeko joined Roma from Manchester City in 2016 after scoring 50 Premier League goals in 130 appearances.
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The 31-year-old was part of the City sides that won the title in 2012 and 2014.
Roma travel to Crotone in Serie A on Sunday while Shakhtar are also next in action on that afternoon, with Paulo Fonseca's side entertaining Mariupol in the Ukrainian Premier League.
Meanwhile, Arsenal face AC Milan tomorrow in the second leg of their last-16 Europa League clash.