Hutter and his scouting team have been alerted to free-scoring Morelos and after watching extensive video footage.
They have now decided to step things up and watch him in the flesh.
Frankfurt paid £7million to make French striker Sebastien Haller their record signing from Utrecht two seasons ago.
But they would need to smash that to persuade Steven Gerrard to sell.
Rangers transfer EXCLUSIVE: Frankfurt want to sign Morelos (Image: GETTY)
Rangers transfer EXCLUSIVE: Morelos is valued at Ibrox at £20m (Image: GETTY)
Rangers transfer EXCLUSIVE: Nice and Cardiff also want to sign Morelos (Image: GETTY)
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The German side are prepared to do that for the right players they feel can take them to the next level.
Morelos has been a major success in his two seasons at Rangers and has netted 28 goals in all competitions this term.
A string of top clubs have already been linked with Fenerbahce, Nice and Cardiff all credited with an interest in the 22-year-old over recent months.
Leicester - who are managed by ex-Celtic boss Brendan Rodgers - and Frankfurt’s German rivals Borussia Dortmund were this week reported to be interested.