Oldest boy Sveinn Aron, 20, is already a professional with Icelandic top division side Breidablik having represented his country at under-19 level.
Then comes Andri Lucas, who at 16 has just moved into the youth team with Espanyol and is regarded highly as forward with real potential.
And finally is youngest son Daniel Tristan, 12, who is making a big impact in the academy programme at Barcelona and who many believe is the best of the lot.
Gudjohnsen told The Sun: “It's a natural thing as a father, I have hit now with my boys, I'd wish them to be miles better than me and top everything I achieved in my career - as long as they are happy and respectful.
“It can be tough, because watching your children play, you want them to do so well and it's tough to take as a parent."