Sharp believes there are four areas in which the Toffees need reinforcements.
The Toffees have signed just one major senior player since Koeman took over as manager, in the form of former Fulham and Southampton goalkeeper Maarten Stekelenburg.
Given the rate at which some of their Premier League rivals are spending, and considering the promise of more funds following Farhad Moshiri's takeover, supporters will likely be a mixture of frustrated and nervous at the relative lack of activity.
The Merseyside club have found themselves floundering in the bottom half of the table for the last two years, and though a change has been made in the dugout to try and address that issue, they surely also need reinforcements in the transfer market.
Sharp is confident that Koeman will make further additions but believes the Dutchman has a lot of work to do, and the former striker claimed there are four positions on the pitch that need addressing.
The Toffees legend told the Liverpool Echo: "I think you look at the forward positions and you have the situation with [Oumar] Niasse going back to Russia or whatever. So I’m sure the forward position is somewhere he will be looking at. I think central midfield we’re well off - but he may want to improve the quality.
"Right-back position for me is one he might have to strengthen. We have Seamus [Coleman] in there and while some of the young kids have been filling in, I don’t think we have a ready-made replacement for Seamus.
"Tyias Browning who is coming back from injury will have a part to play, but I think the rest of the season with just one right-back would worry me. You would also want to look at the goalkeeping situation."
As alluded to by Sharp, Everton supporters may feel that they desperately need another striker to compete with top scorer Romelu Lukaku with Niasse's £13 million signing having proved a dismal failure this far.
There is also a lack of competition for Coleman at right-back, whilst Stekelenburg and Joel Robles are the club's only two senior goalkeepers.
It appears as though Koeman is on the verge of adding to his central midfield options, however, with Aston Villa star Idrissa Gana Gueye seemingly set to sign in the coming days.