Cockerill hopes Arundell's brilliance can spark English response
The 20-year-old wing, whose six previous international appearances have come off the bench, faces a baptism of fire against an Ireland side bidding to win the Grand Slam on home turf at Lansdowne Road.
However, such is Arundell's ability to rip through defences, the England camp hope that is what is needed to spark an immediate positive response from the team after their 53-10 hammering by France last Saturday.
"He can score something from nothing," said Cockerill at Friday's press conference.
"We saw that in Australia last summer in the first Test and now he has the opportunity to start the game in a white-hot atmosphere.
"We think he is ready to come in and make a difference.
"One hundred per cent he has a big future.
"He is a finisher. We have seen that at his club and we have seen that at Test level in parts. Hopefully we will see that tomorrow."
England captain Owen Farrell, restored to the starting line-up after being on the bench for the French clash, concurs Arundell is a special talent.
"You see people who do it at club rugby week in, week out, but do not always find it as easy to do it when they come into the Test team and in training," said Farrell.
"It seems like - we saw this in Australia, in the summer - it seems like every time he touches the ball people expect him to do something good. And he doesn't normally disappoint."
'His rules'
Arundell is just starting out on his Test career but Cockerill, who is leaving the England set-up to take up a role at Top 14 side Montpellier, was keen to lavish praise on veteran prop Dan Cole.
The 35-year-old Leicester stalwart will win his 100th cap if, as likely, he comes on as a replacement on Saturday.
"To play hopefully his 100th Test tomorrow is testament to how good a player he is and his resilience to stay in the game long enough to do that," said Cockerill.
"He's gone back to his club after being dropped and played really well for them.
"You wouldn't want the World Cup final (the defeat by South Africa in 2019) to be your last game would you, if you were Coley.
"So he's worked really hard to get the opportunity to get back into the squad.
"We'd love to celebrate his 100th cap with a proper performance."
For Farrell, aside from hoping to restore some pride with a win over the Irish, there is the uncertainty of what shirt his sons Tommy and Freddie will be wearing come game time.
The two boys are staying with his parents, Ireland head coach Andy and mother Colleen, in Dublin for the weekend having travelled over on the ferry on Thursday - though granddad is at the Irish team hotel.
Farrell seemed taken by surprise when he was told they had been at Ireland's final training session at Lansdowne Road earlier on Friday.
"I didn't know that, I genuinely didn't know that," he said laughing.
Farrell said he hoped to see them in England shirts when he runs out on Saturday.
"I have not spoken about it," he said.
"I assume and I do still assume that they will be wearing England jerseys, but I see they are trying to sway him.
"I guess it's his rules this weekend, so far."