The Bon Jovi guitarist and the band's frontman have exchanged guarded words since Richie quit their 'Because We Can' tour in April citing ''personal issues'' but he thinks they will eventually be able to resolve their problems and he will return to the group.
The 53-year-old rocker told gossip website TMZ.com: ''It'll all work out in the end.''
Richie is disappointed by reports that ticket sales for the band's tour have been affected by his absence but acknowledged that the group have gone through difficult times before and were able to get through them by going to therapy together.
He said: ''I feel bad for the fans... I love my fans but you know it's going to work itself out. It'll happen. You know, like I said, Jon and I have a relationship of 30 years and we rely on each other.''
The guitarist recently hit back at Jon after he appeared to claim that Richie wasn't a vital part of the band.
He said: ''Life goes on, so if someone chooses not to be here... unlike if this were, God forbid, The Edge, and he for some reason couldn't make a U2 show, [then] it would be very difficult to just step in.''
According to reports Richie then sent Jon a short and scathing email, reading: ''Hire The Edge.''
A band insider added: ''Richie was so p****d off and insulted with The Edge comment that he couldn't bite his tongue any longer. He sent Jon an email, but Jon did not respond.''
The BBC drama starring Aidan Turner returns to BBC One on September 4th.