The former midfielder joined Chelsea in 2017 from Leicester City for £45m, but found himself sidelined given the talent in the Blues engineroom.
He told Rio Ferdinand’s podcast: "Looking back actually, I remember Azpi tried giving me the heads up about this when I was in that second season.
"So I was in there with Cesc (Fabregas) on that Sarri first pre-season, so it would've been me and Cesc I think, Kova (Mateo Kovacic) might have been there, and they were trying to bring Jorginho in.
"N'Golo (Kante) was obviously there wasn't he? So N'Golo, Cesc and me, I can't remember if Kovacic was there at the time.
“But then (Cesar Azpilicueta) Azpi's like, 'Drinks, if they bring Jorgi in, which they're going to, they want to, you need to think about what you want to do here.'"
After rejecting a permanent move away upon Sarri's appointment, Drinkwater recalled a loan proposal was also put to him.
He said, "So Sarri's English, again, when he came, wasn't the best... That first window after that summer, it was like the last day of the window.
"My son was a year old here as well, so I've got stuff off the pitch that I'm focusing on as well.
"(Gianfranco) Zola came and saw me, and said, 'Drinks, the gaffer would like to see you.' So I was like, 'Yeah, buzzing, sweet.' Didn't expect anything from it.
"I came up and he's like, 'I think you should go on loan.' So I was like, 'What? What time is it?' I was like saying, 'I've got an hour to get a club, what do you mean?'
"And he's like, 'No no, loads of like... I've got a Serie A team, loads of teams asking about you.' (I'm) like, 'Nah nah, I ain't going out of England, are you mad?'
"Just had a baby, I'm a footballer but I'm a dad, I ain't going anywhere. And he's like, 'Well, you might get frustrated.' I was like, 'Well, I'm going to get frustrated aren't I? This is a joke.'"