The 22-year-old is set to join The Sky Blues in a deal worth £17 million, per the BBC.
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The Switzerland centre-back will sign a four-year-deal with the club for an initial fee of £15.4 million which a further £1.7 million in add-ons.
It has been reported that Amenda has been swayed to join Coventry by boss Frank Lampard, as his side gears up to play Premier League football in the 2026/27 campaign.
Amenda was included in a Swiss squad that reached the quarter-finals of the World Cup, but he did not make an appearance at this summer's tournament.
He made 24 appearances for Frankfurt last season in the Bundesliga, and is now set to make the switch to England to play in the Premier League under Lampard next season.