Lookman followed up his goalscoring performance in the FA Cup victory over Lincoln City on 5 January with another dynamic display in Everton’s 2-0 Premier League success against Bournemouth on Sunday.
The former Charlton Athletic player’s direct running and lightning-quick feet regularly put the Cherries defenders on the back foot at Goodison Park.
Lookman’s sharp, incisive passing also caught the eye, most notably when he slipped in Dominic Calvert-Lewin in stoppage time – his fellow England Under-21 international duly rifled home to secure maximum points for the Blues.
Lookman’s performance earned praise from Everton boss Silva, who described him as “a fantastic player who will get better and better”.
Keane echoed the manager’s views and believes the 21-year-old has the attributes to become a key player for Everton.
“Everyone can see that quality he’s got in training,” he said.
“He’s had to be patient this season and wait for his chance.
“I think he showed what he can do today, and I think he’s shown it in glimpses throughout the season.
“He’s a very talented player and he’s only young, too, so he’s only going to get better. I think he’s got a lot of experienced players around him to talk to, to give him advice.
“The world is his oyster if he can keep improving.”
Keane was in typically commanding form against Bournemouth, helping to lay the platform for a victory that saw Everton move to within two points of seventh place in the Premier League.
The centre-back made 11 clearances during the match – more than any other player on the pitch.
The 26-year-old’s influence on the game was also highlighted by the fact only the excellent Lucas Digne had more touches of the ball for the Blues.
And with the game on a knife-edge at 1-0, Keane made a vital challenge on former Everton man Dan Gosling late in the piece, timing his tackle to perfection to thwart the midfielder as he bore down on goal.
The England defender believes the strong competition for places in the team is driving up performance levels.
Keane is battling it out with Kurt Zouma, Colombia international Yerry Mina and Club skipper Phil Jagielka for a starting spot.
“It’s a tough decision for the manager, who to pick every week,” he said.
“Whoever I have played with, I think we have formed a good partnership.
“I’m really comfortable playing with them all.
“Yerry and Kurt are both fantastic players. Me and Kurt got the shirts this week and we did well and kept a clean sheet.
“There is a lot of competition for places in that position – I think that’s what keeps us going. It pushes us on and helps us to get better.”
Keane says the Blues are determined to build on their victory when they take on Southampton at St Mary's Stadium on Saturday.
He is confident the team can put together a series of results that can propel them up the Premier League table.
“We showed signs of what we are capable of [against Bournemouth],” said the defender.
“We just want to get on a good run and see where it takes us. We did it earlier in the season, we want to get on that run and be more consistent. Consistency is the key for us and now.
“Results breed confidence. Hopefully we can now grow and get better.
“We’ve got to keep learning and keep improving. I’m included in that.
“If we get a bit more consistency, we’ll climb the table.”