Radio Silence but with a warning

So I have finished the third round of interview (out of total 4) in this big company. After the last interview I was told I have been given a thumbs up only formality remains and after that a pool of selected candidates will be made. Which he said he really think would include me. But THIS WILL TAKE SOMETIME. I will hear back on a say Thursday or Friday. It is Wednesday now. Should I text him. I mean he did warn me but I was also assured that he will respond to my emails.

I dont want to sound needy or clingy. Probably sending email might show my interest in the job. What should I do.

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