Essex coach Grayson took the side to Barbados during pre-season
Essex say they have lined-up another overseas bowler to sign after recent attempts to capture the signatures of Peter Siddle and Tim Southee failed.
The as-yet unnamed player will not be available for the County Championship opener against Kent.
But it is hoped a deal will be completed in time for the match at Middlesex on April 14.
Coach Paul Grayson told BBC Essex: "Hopefully this new guy will come in and do a good job for us."
Australia's Siddle had agreed to join Essex but the deal to sign him broke down for personal reasons.
New Zealand fast bowler Tim Southee was then close to moving, but instead agreed a move to the Indian Premier League.
In a live BBC Essex phone-in, Grayson also confirmed that Ravi Bopara had turned down a late switch to the Rajasthan Royals in the IPL.
"He was asked to go back and play in the IPL, he could have gone and made some good money," he said.
"He's determined to get that England spot back. With Paul Collingwood retiring I think Ravi would be the best choice to bat either five or six."
Chief executive David East also took calls from supporters and confirmed that plans to re-develop the County Ground in Chelmsford are currently on hold.
"The original funding for the project has now vapourised.
"We're currently very busy with our development partners looking for alternative funders, and also looking at the possibility of alternative phasing of the project."
Essex have been granted planning permission for the upgrade, which includes an increase in capacity from 6,000 to 8,000.