The sources identified three of the four bidders as France's Amundi, Europe's biggest asset gatherer, a consortium led by Poste Italiane and top Italian player Assicurazioni Generali.
One of the sources said the fourth suitor was expected to be French insurer AXA, according to Reuters.
The sale of Pioneer is part of a broader effort by UniCredit to improve its capital ratios with analysts estimating it could need to raise as much as 8 billion euros through asset sales and an expected share issue.
The Italian bank aims to net around 3 billion euros ($3.4 billion) from the sale of Pioneer, sources have said.
"Amundi's offer is quite high," one of the sources said, adding however that this could change after the due diligence process.
Binding offers are due by the end of October. UniCredit, which is advised by JPMorgan and Morgan Stanley, hopes to clinch a deal before presenting a strategic plan due by the end of the year.
Amundi, AXA, Assicurazioni Generali and UniCredit declined to comment. Poste Italiane was not immediately available to comment.