Independent directors are recommending the offer, which is being made by funds controlled by shareholder DBAY Advisors.
The offer values Nash at £98.7mln. DBAY already controls 26.1% of Harvey Nash shares, while directors speaking for 1.72% have also agreed to the offer.
Approval for the offer is required by 75% of all shareholders to go ahead.
Julie Baddeley, chairman, said while Nash had a strong future as an independent company, the wholly-cash offer was an attractive value.
Shareholders will also get one interim dividend of 1.75p per share.
DBAY took a significant stake in Nash in February 2017.
David Morrison, the firm's Investment Director, said it was an opportunity for Nash to strengthen its leading position in the specialist technology recruitment and outsourcing markets.