The musician and the band's frontman have exchanged guarded words since Richie quit their 'Because We Can' tour in April citing ''personal issues''.
Jon first revealed Richie was suffering with an issue has been through before, sparking speculation he was referencing the axeman's last stint in rehab, for alcohol abuse, in 2011.
The singer later hinted he didn't think Richie was an integral 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 RadarOnline.com, Richie has now 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.
''Jon hasn't called Richie once since this all began. It would seem that he does not want the band back together.''
Richie, fed up of Jon's ''trash talking'', recently told the MailOnline he would love to bury the hatchet and return for the 'Livin' on a Prayer' band's upcoming show in London's Hyde Park.
He said: ''I would love to be in London... let's see what happens. I love my fans, I have no personal problems. I am a happy man!''
He has previously said: ''[The fans] have paid money to see Bon Jovi and right now, they are not getting the whole deal.''