There is nothing to suggest Jesus was saying to look out for being who say those two things together.
He replied: "Watch out that you are not deceived. For many will come in my name, claiming, 'I am he,' and, 'The time is near.' Do not follow them.
Plenty of people have claimed to be Jesus; does it follow that if they don't claim it is the due time they are worth listening to?
And note the use of quotation marks around the statements. Even the NWT has them. If it was one statement it would read:
For many will come in my name, claiming, 'I am he, and the time is near.'
Then you might have a point.
But it doesn't.