Most native speakers probably would consider it inappropriate to delete the relative pronoun "that" here.
It's not really a matter of "grammar" as such, because there are many contexts where that, who, which, etc. can (and often, should) be deleted. But on average, such deletions aren't so common in formal registers - so much so that less competent writers are sometimes guilty of including too many.
To illustrate the formal/informal divide in respect of this construction, consider...
There is a man wants [to meet you]. formal - 6 results in Google Books
There's a man wants [to meet you]. informal 3580 results
There is a man who wants [to meet you]. formal, "correct" - 120,000 results
Note that one shouldn't take this idea of "that" = "correct" too far. Consider...
1: There was a girl I knew at school [who used to blah blah]
2: There was a girl that I knew at school [who used to blah blah]
There are at least a handful of results for #1 there, which sounds like normal fluent English to me. And whilst I don't think #2 is "wrong" (some may actually say only #2 is "right"), I'd have to say it sounds a little "over-precise" to me. And there are no results for it in Google Books, which I think backs me up on that.
EDIT: Apart from the not really a matter of "grammar" bit, I stand by what I've said above, and I think it's relevant to note that the rule You can't omit that when it's a subject isn't universally observed in casual/dialectal speech. But overall, I'm in no doubt @snailboat's answer is more accurate (and concise) than mine.