In an interview with the daily Il Sole 24 Ore, Arnold said Marchionne, who is already non-executive deputy chairman at UBS, would be the natural leader of the Swiss bank's supervisory board.
"The ideal would be that he become chairman for three months so as to guarantee the search for a new chairman, who should be a top-ranking banker," Arnold said.
Arnold added that a favorable outcome to the corporate governance issue at UBS "would prompt us to significantly increase our stake".
Olivant owns 0.7 percent of UBS.
Arnold, a former head at the Swiss bank, has called for a shake-up of UBS' board and reports have said his strategy is attracting support from some shareholders.
Yesterday La Repubblica reported that Marchionne said he intends to remain at Fiat until at least 2012.