Speaking to Marketing, Draper said he was mindful of fans' concerns about the £790m takeover of the club by US tycoon Malcolm Glazer, but insisted a boycott would not be helpful.
'We all want United to be a successful team, and the club's commercial enterprises support that aim,' added Draper.
However, the chairman of the Independent Manchester United Supporters Association, Jules Spencer, said fans should switch their Vodafone contracts, avoid buying Nike products and encourage their friends and family to do the same.
Manchester United has 1.5m UK fans, with as many as 75m worldwide. However, the club and its sponsors doubt significant numbers will join a boycott.
Apart from Vodafone and Nike, all United's commercial partnerships, which include Budweiser and Fuji, expire at the end of next season. Draper said he was talking to existing and potential sponsors in the US, Asia and Europe, and would be announcing new deals shortly.
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