Lascelles played 90 minutes of the Premier League clash at the Emirates on Monday evening as Arsenal clinched a 2-0 win to climb to third in the Premier League.
The 25-year-old has developed into one of Newcastles best players since signing from Nottingham Forest in 2014 and has been linked with some of Englands biggest clubs.
Lascelles was not at his best in north London on Monday but, speaking before the Arsenal clash, Manchester United legend Cole said: I like him.
Hes a young, promising centre-half who could play a highest level if given the opportunity.
Hes a great size, has good pace and seems very composed on the ball. If youre the captain of a club like Newcastle at such a young age, thats some going.
Asked by Jamie Carragher whether Lascelles could play for a club like Arsenal, Cole responded: Yeah. I think he could play at Arsenal for sure.
Despite Arsenals win and clean sheet against Newcastle, Carragher remains concerned about the teams defence.
And the Liverpool legend believes Unai Emery will need to spend big on a defender this summer.
He said on Monday Night Football: Theres no doubt that the defence is the weakness. Emery hasnt been able to solve the problem.
The only way hes going to solve that is going into the transfer market. We know where the problems are.
Im yet to be convinced by the back three. One, or maybe two defenders need to come in.