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"We're hopeful because there is a willingness from both parties. Both parties want to have an agreement, so we're optimistic," said Paul Foortse.
"It's a matter of going ahead or not - we expect that it should be finalised either way by the end of the week."
Newcastle have been chasing a new striker this summer as they look for a long-term replacement for Alan Shearer, who is retiring at the end of this season.
Southampton's James Beattie has also been linked with a move to St James' Park.
Kluivert was released by Barcelona at the end of last season and is available for free, meaning his wages would be the only sticking point.