The attacker is still under an indefinite suspension for ‘verbal insults’ targeted at the coach during the Fifa World Cup in Brazil.
The 31-year-old, together with Sulley Muntari, was sent away from camp ahead of the final group game against Portugal, and according to the Ghana Football Association, only an official apology could see his return for national duty.
Discussions about a possible Ghana comeback for Boateng has resurfaced following his sensational transfer to Barcelona on Monday.
“Kevin-Prince Boateng is a Ghanaian and currently he is playing very well," Appiah told Asempa FM.
"If you look at our striking options, we have always relied on [Asamoah] Gyan, so it's about time we all checked and got at least four strikers that we can always rely on.
“Kevin is one of the good strikers as I have said, but in Brazil, he and Sulley were suspended by the FA for their unruly behaviours.
"I think Sulley has written a letter to apologise and looking at how Kevin is playing now, if he should write a letter to apologise, I will invite him because it is about the country [and] not about any individual.”
Born to a German mother and a Ghanaian father in Berlin, Boateng switched international allegiance to represent the Black Stars at senior stage in 2010 after representing the European nation at youth level.
He has 15 caps and two goals for the four-time African champions.