Osadebe has started the last two games and opened his account for the season as the Saddlers got past Northampton Town on penalties in the EFL Trophy last week.
He then impressed in the victory over Salford City in League Two at the weekend – going close with a free-kick – and Taylor feels he has lots of potential.
“I was really pleased for him to get the goal,” said Osadebe.
“His run was fantastic. He does that in training.
“Now, it’s about continuing to do that in match situations.
“It’s up to him and all the other players, let’s see how far they can go as a team and as individuals.
“I’m of the opinion that we are at the tip of the iceberg with Emmanuel.”
One of the few players to stay at the club amid a summer of change, Osadebe has previously been praised by Taylor.
The 24-year-old Irishman – referred to as ‘Paddy’ by his team-mates – has been hailed as an ‘extremely good’ talent who is ‘hungry’ for success at Walsall.
Now, Taylor wants to see him display his ability on a consistent basis by finding the net and providing assists in healthy numbers, having managed one of each so far this campaign.
On where Osadebe can improve for the Saddlers, Taylor said: “It’s decision-making. That’s the crux of it.
“He picks up some wonderful positions and receives the ball on the half-turn. His awareness is very good.
“If there’s something he needs to improve upon, though, it’s that final pass and final decision.
“What I will say is that he’s working extremely hard on a daily basis.
“What I like about Paddy, too, is he asks a lot of questions.
“It’s not criticism when you’re coaching him.
“He doesn’t take things personally and he’s desperate to learn, and that shows me he’s a player we’re very fortunate to work with at the football club.
“Having said that, I think that his return this season hasn’t been good enough.
“He’ll most definitely back that up.
“He needs to score more goals and get more assists.”