The 49-year-old Ayrshire businessman left the Labour Party in the 1980s and twice ran as a candidate for the Westminster seat of Kilmarnock and Loudoun without success.
Ian Blackford took legal advice on defamation proceedings after being suspended as treasurer at a meeting of the SNP's national executive last month.
Speculation has mounted that Mr Salmond's surprise announcement that he was quitting the national convener's post after 10 years was linked to the dispute with Mr Blackford.
A managing director with an international investment bank, Mr Blackford said that Mr Salmond had made statements which were damaging to his professional reputation.
He said the leader had accused him of incompetence in his stewardship of the party's finances, of overspending at the Scottish election and of destabilising the party by leaks to the media.
The SNP is reported to be £400,000 in debt and its headquarters in Edinburgh are for sale.
"This is something which has blown up over the last few weeks but I don't see it has led to Alex's resignation.
"If I do take any action against Alex, that is on a personal basis and is not attacking the party in any way."
He plans to take his fight to the party conference in September, where members will vote in the leadership contest.
Mr Blackford is supporting Alex Neil, the only candidate so far to declare his hand.
Neil 'confident'
Deputy leader John Swinney is the bookmaker's favourite for the post, but Mr Neil said he was confident of his chances of success.
He told BBC Radio Scotland: "It's very important for people who are intending to stand to let the party know as soon as possible and I think it's perfectly fair to do that.
"Originally the nominations were to close on Friday, but now that's been extended by another two weeks, but I've made it clear that if there was a vacancy then I would be interested in filling it."
The 49-year-old Ayrshire businessman left the Labour Party in the 1980s and twice ran as a candidate for the Westminster seat of Kilmarnock and Loudoun without success.
The left-winger is seen as representing the fundamentalist wing of the party which favours fast progress towards independence, whereas Mr Swinney is seen as being more of a gradualist.
Asked about the differences between himself and Mr Swinney, Mr Neil said: "There are differences of strategy and tactics clearly, but there are no major policy differences.
"When you are electing a leader you are looking at the qualities required for leadership in terms of team management, in terms of vision, in terms of energy, in terms of experiences."
The battle for the nationalists' hot seat began just hours after Mr Salmond unexpectedly announced resignation after a decade in the post.
He told a news conference in Aberdeen that it was time to step down and let "one of the many talented people in the party" take over.
As yet, Mr Swinney has not declared his intention to run. However, he is expected to do so within the next few days.