Bids for the vegetable juice maker have come in at between $1.5bn and $2bn according to a report by Bloomberg, which said Bolthouse has asked for final bids this week.
That would mean a sale of the company is likely to be agreed by the middle of the month.
Bloomberg said previous management members at Campbell had considered a bid for Bolthouse but decided against the deal.
The new interest has arisen since Denise Morrison took over from Doug Conant as Campbell CEO last year.
Bolthouse, which was bought by Madison Dearborn in 2005, has EBITDA of more than $150m, with about two-thirds of profits coming from its carrot-related businesses.
It also makes fruit drinks and dressings.
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