The former England striker is currently a free agent after being released by Manchester United at the end of last season and is on the lookout for a new club.
The 32-year-old had the best spell of his career as a Liverpool player, which Sharp admits could result in a frosty welcome from some supporters.
"I'm not too sure how the fans would feel about Owen," Sharp told talkSPORT. "There's a bit of discontent [at the prospect of signing him].
"We need to strengthen the squad. The top 14 [players] are a match for anybody, but underneath that if they get injuries they might be struggling.
"Owen's name keeps coming up, but he hasn't done a pre-season so he would probably be four or five weeks behind everyone else."
Everton beat Owen's former employers Manchester United 1-0 on Monday.