Wilshere enjoyed one of the most active years of his injury-prone career during a loan spell at Bournemouth last season, and the bookmakers have now made the Hammers favourites to sign the 25-year-old from Arsenal.
However, West Ham have made no secret of their desire to bring in more attacking players this summer and Gold suggested that they do not need to strengthen much elsewhere.
"We are interested in all good players but we have to face the facts here - we have got good midfielders," he told talkSPORT.
"We have got a good defence, we have got good midfielders, we have got good wingers. We need strikers and that is the key to everything for this season so we are focused first and foremost on bringing in two strikers."