The world's first multi-national classical crossover group - comprised of Urs Buhler, Carlos Marin, David Miller and Sebastien Izambard - have worked with the 27-year-old singer/songwriter's regular producing-and-co-writing partner Steve Mac from the very start of their career, since their debut self-titled record in 2004.
And the group - who released the Spanish version of Adele's 'Hello', 'Hola', this year - have revealed they would love the chance to get into the studio with the 'Shape of You' hitmaker and want him to get in touch.
Speaking exclusively to BANG Showbiz, the group's 45-year-old tenor David Miller said: ''We would absolutely love to work with Ed Sheeran, are you kidding?
''There wouldn't be anyone that would say no, I think it would be absolutely wonderful.
''Steve Mac is one of the best producers we have had the chance to work with, and I am super happy that he has been able to do this record with Ed Sheeran ['Perfect'].
''Tell him to give us a call, we are available.''
Meanwhile, the band are set to head out on a tour of castles in the UK, entitled 'Timeless: The Castle and Country Tour', in support of their LP 'Timeless', which is released on August 17.
The run kicks off at Euston Park in Thetford, Norfolk, on July 5, before heading to locations in Berkshire, Wales, Edinburgh, Warwickshire, Northumberland, Chichester, Leicestershire and Yorkshire.
Il Divo will also headline London's Greenwich Music Time on July 8.
For six of the shows the group will be joined by special guest Michael Ball.
The musical theatre star - and one half of duo Ball & Boe with Alfie Boe - said: ''I'm delighted to be performing at these incredible venues with Il Divo.
''The audience are in for a real treat and I'm looking forward to sharing these special moments with the fans. See you this summer!''
Tickets are on sale now from ticketmaster.co.uk.
Ill Divo's 'Timeless Castle and Country Tour' dates are as follows:
July 5, Thetford, Norfolk, Euston Park
July 7, Englefield, Berkshire, Englefield House
July 8, Greenwich, London, Greenwich Music Time
July 10, Cardiff, Wales, Motorpoint Arena
July 13, Castlehill, Edinburgh, Edinburgh Castle
July 14, Alcester, Warwickshire, Ragley Hall
July 15, Alnwick, Northumberland, Alnwick Castle
July 17, Stansted Park, Chichester, Stansted Park
July 20, Grantham, Leicestershire, Belvoir Castle
July 21, Scarborough, Yorkshire, Scarborough Open Air Theatre