Lawyers for Father Matthew Despard, who has been suspended since last November, said he would make overtures to his new hierarchy.
He faces legal moves to evict him from his parish house and has already lost one legal battle over the disagreement.
Action under church judicial process, or canon law, is also under way as a result of the publication of the allegations made in his best-selling memoir Priesthood In Crisis.
His lawyer, Hugh Neilson, said there had been "no shortage of olives branches" in correspondence to and from new Bishop of Motherwell Joe Toal during his time as administrator for the diocese, adding that Father Despard "respects and honours" the senior cleric and was seeking to "resolve the breach in relations".
Mr Neilson said Father Despard was seeking a "brotherly and Christian way forward" in the row which has split the Catholic parish of St John Ogilvie in Blantyre, South Lanarkshire, and the priest would "make what he regards as suitable overtures respecting the new bishop in the hope that matters can be resolved without unnecessary court action".
A spokesman for Bishop Toal said he welcomed the chance of an amicable resolution to the issue of the parish house, with the offer of alternative accommodation in the area open.
However, it is understood the canon law action has to run its course and is no longer in the hands of Bishop Toal.
That investigation will also look at the claims made by the priest.
Father Despard was suspended amid dramatic scenes at the church last November after the canon law process was launched.
The 48-year-old priest published his book in the aftermath of the resignation of Cardinal Keith O'Brien, who was relieved of his duties after admitting decades of sexual encounters with other clergy.
In the book, Father Despard claims he was approached inappropriately as a seminarian and said trainee priests who spurned advances of others were bullied. He also complained of having his claims ignored. The book has since been withdrawn by Amazon, following the legal threats by individual priests who claimed to have been defamed.
The church has already won a legal battle for access to the parish house, with a further action planned after a notice to quit expired on Thursday.
Mr Neilson said: "Overtures will be made to the new bishop to see if there can be a brotherly and Christian way forward that doesn't involve the church in any further adverse publicity and can see honour satisfied and truth recognised.
"The appointment of Bishop Toal is something that Matthew Despard requires to and does respect and will honour."
A spokesman for the new bishop said: "Bishop Toal has offered to meet Father Despard on a number of occasions in the hope that matters which have unfortunately become the subject of legal proceedings could be resolved.
"He continues to hope this meeting will happen and that Father Despard will agree to do what Bishop Toal has asked of him."