Carrick was named as Man United’s interim manager following the dismissal of Ruben Amorim and disappointing tenure of Darren Fletcher.
The former United midfielder has since won both of his games at the helm, first against local rivals Man City and now league leaders Arsenal.
Despite Carrick’s impressive start, Keane doesn’t believe he should be the man to take over on a permanent basis.
When asked about whether Carrick should be given the job, he told Sky Sports: "You're being silly now. Two great performances, but anybody can win two games.
“It's what he does until the end of the season, and even if they do get into fourth I'm not convinced he's the man for the job. Absolutely not.
“I think they need a bigger and better manager. But he's got the opportunity. What a chance for him and he's taken it, so fair play to him."