The Croatian endured a frustrating campaign for the Toffees last season, only managing to find the net seven times in the Premier League.
The summer signings of Arouna Kone from Wigan and Gerard Deulofeu on-loan from Barcelona means that new manager Roberto Martinez has an increased number of striking options to choose from, with Jelavic and Anichebe also hoping to lead the line.
Jelavic made an impressive start to life at Everton upon his arrival in January last year and Osman believes that the increased rivalry for places will encourage the 27-year-old to rediscover his early form.
"I think, for the most part, strikers relish competition," he told the Liverpool Echo.
"It makes them work harder; it makes them strive to improve themselves every single day."
The striker had been on an extended break after being away on international duty, but he returned ahead of schedule to watch Everton's friendly defeat against Austria Vienna.
Osman added: "Jela turned up to watch us. He tried to keep it a secret and came as a surprise before travelling back with us. Then he'll be right back on it on his first day of training.
"He seems happy. I don't know whether it's because he's had a good summer or he's just happy to see us. He seems lively and raring to go."
Osman also insisted that despite Jelavic's woes in front of goal last season, the former Rangers man was always fully committed to the Everton cause.
"It can happen for anyone - not just the foreign lads who have come over here," said Osman.
"Any player can have a tough season or a dip in form. The one thing you can't let up is your commitment and you can always give that.
"He showed what he was capable of in that first three or four months when he came over, and we haven't got anything to complain about what he did last year because he always worked as hard as he could for the team. When you ask someone to go over that white line and they give you everything you can't really complain.
"Looking at the bigger picture - the most successful clubs are the ones who have an abundance of choices in strikers and we're now getting there with quite a few options. It's better for us."