The party's ruling national executive committee (NEC) is due to discuss Bolton's status at a meeting next Sunday.
However, Oakden suggested Bolton could quit before then which would mean Ukip being forced to elect its fourth leader in less than two years.
He told the BBC's Sunday Politics programme: "I think it is very clear that Henry is increasingly in a position where he has got some difficult decisions to make. He knows that. He and I have spoken regularly over the weekend as recently as this morning.
"I know that he is very focused on those decisions today. He intends on making those decisions today and I am sure whatever he does will be in the best interests of the party."
He added: "They will consult with the leader a week today (Sunday), if he is still the leader at that point, and they will collectively make a decision on what to do going forward."
In a series of messages published by the Mail on Sunday, Marney referred to Markle as a "dumb little commoner" with a "tiny brain".
She also used the word "negro" in the exchange and said "this is Britain, not Africa" during a discussion about the royal engagement.
When her friend suggested her comments were "racist", Marney replied "lol so what".
Bolton said on Sunday that Marney had been suspended from Ukip "immediately upon us receiving this information".
But the incident has prompted calls for Bolton to resign.
Bill Etheridge, a Ukip MEP and former leadership contender, threatened to quit as a party spokesman if Bolton does not quit.
He said: "It is quite apparent that Henry does not have the experience, the political nous or the correct advice to deal with the issues that he faces.
"As I say, I have absolutely no comment to make about the man's personal life, I am commenting entirely based upon his professional performance as a political leader.
"Quite frankly the time has come for Henry Bolton to resign as leader of Ukip.
"He must go. He must go quickly. He must go as quietly as possible."
Etheridge said he would stand down from his party spokesman role if Bolton "insists on prolonging this agony".
Meanwhile former Ukip leadership candidate Ben Walker called for Bolton to resign, accusing him of having "deeply flawed judgement".
Marney said in a statement: "The opinions I expressed were deliberately exaggerated in order to make a point and have, to an extent, been taken out of context. Yet I fully recognise the offence they have caused."
Bolton left wife Tatiana, 42, prior to his relationship with Marney becoming public in early January.
He was elected Ukip leader last September.