The Daily Mail says Grant has delivered a coded warning to his squad about their off the field behaviour in the wake of a raft of lurid stories surrounding the private life of Ashley Cole.
Outlining his expectations, Grant said: "They need to be a professional; a professional is not just what you think. A professional is also a state of mind, it's not just if you drink or you don't drink, that is obvious.
"It is many things about players, how you look at the game, how you look forward, if you live in the past too much. In football you need to choose players, not just based on their quality but on their character.
"I say to my players that I will test them on how they behave on the very good days, whether they still want to learn, whether they still want to focus or if they think they know everything.
"And also on the very difficult days, do they take responsibility or say everyone else is to blame? And do they learn from this? I examine their behaviour when we're winning and losing."
Cole missed Chelsea's FA Cup victory over Wigan on Saturday having been late for training the previous day after the stories about his marital strife broke, with reports suggesting he spent the day with his lawyers, although Grant insisted his absence was simply a case of him rotating his squad.
Asked whether Cole was mentality ready to return tonight, Grant replied: "No problem, he's a full professional, he's ready. But I am trying to rotate the players and keep them fresh because we have a lot of games. This is position where we can do that."