You are trying to use a passive voice. In the passive voice, the subject of the sentence is the thing being acted on instead of the thing acting. So if you said simply, "He will be contacted three times," that would be a good and valid sentence. "He" is the thing being contacted.
If you were using the active voice, you might say, "We will try to contact him three times." That would also be good and valid: "We" is the subject, and the thing we are doing is "trying", and specifically what we are trying is "to contact".
But you can't switch this complex verb, "try to contact", to the passive, "He will be tried to be contacted." The problem is that "he" is not "being tried". That is, we are not trying "him", we are trying "to contact". So you can't say, "He is being tried". You want to say that the contacts are being tried, not him. To the best of my knowledge, there is no way in English to turn "verb-1 to verb-2" into a passive voice. You could convey the idea by saying, "Three contacts with him will be tried." I think that's an awkward sentence, but it's grammatically valid. I'd prefer to say, "Three tries will be made to contact him" or "Three attempts to contact him will be made". Or switch it to the active voice: "We will try to contact him three times."
Note that the structure you are using would be valid if "he" was properly the thing acted on by both verbs. For example, you could say, "He will be asked to be added to the list." This is valid because "he" is the thing being asked, and "he" is also the thing being added.
Side note: Perhaps I should make clear that "tried" IN THE SENSE THAT YOU ARE USING IT IN THIS SENTENCE is not acting on "he". The English word "try" can mean "attempt", which is how you are using it here. A person cannot be attempted. What would that mean? But "try" can also mean "put on trial", as in a courtroom with a judge and jury. In that sense, you certainly can try a person, and a person can be tried.