The Terriers made a move for the former Manchester United striker on Monday night as they seek a replacement for the sacked Simon Grayson, but saw that request initially rejected.
The Sky Blues have now given their manager permission to talk to the Championship club.
A statement read on the Huddersfield website: "Huddersfield Town can confirm it has reached an agreement with Coventry City, who have granted permission for the club to speak to Mark Robins.
"Talks will commence immediately this evening."
Coventry confirmed they had reluctantly given Robins permission to talk to Huddersfield about a move to the Championship club.
Sky Blues Chief Executive Tim Fisher told the club's official website: "We have had more than one club interested in Mark in the last few weeks and we have made every effort to ensure he stays with us.
"We talked to him at length today and he met the owner. Once we had done everything we could and it was obvious that he was still interested in talking to Huddersfield, we had no choice other than to let him do so.
"We are just hoping that when he weighs up his options and opportunities, he will see the great progress to date and the support he has from fans and management alike, coupled with the potential in Coventry, and decide to stay."
Robins has only been in charge at the Ricoh Arena for 33 games, but has led the Sky Blues on a superb revival and they are in play-off contention in League One.