Liverpool star Coutinho and Southampton’s Van Dijk each handed in transfer requests to try and get out of their respective clubs.
Sanchez hoped Arsenal would sell him on deadline day after refusing to sign a new contract.
In the end none of the deals went through, with Liverpool and Southampton refusing to sell, while Arsenal couldn’t get a replacement for Sanchez.
And former Liverpool and Tottenham player Danny Murphy says the trio’s team-mates will not have a problem when they return to the field for their current sides.
“Occasionally, some of the lads are glad to see the back of players for whatever reason,” Murphy told the BBC.
“But that is not the case with Van Dijk, or Coutinho and Sanchez for that matter.
“From the players I have spoken to who know them, they are all decent guys who train well and work hard.
“They are all very good players too, of course. That is another reason their team-mates will want them back in contention for selection.
“With Coutinho at Liverpool, for example, his team-mates will know that when he has played for the club he has always given his all and the fact that it was Barcelona who were in for him completely justified his desire to leave.
“None of them would have begrudged him one bit for going there and it was not about the money for Sanchez, either. If it was, he would have signed the new contract he was offered.
“For me he is the Gunners’ best player by a mile. He seems to work harder than everyone else and he gets frustrated that not all of his team-mates have the same standards or work ethic.
“He wants to move on to win trophies and, if he was my team-mate, I would understand why he was unhappy.
“I don’t think Arsenal fans should worry about Sanchez’s attitude now either, because he has the kind of character where he has to give 100%.
“He cannot play any other way and, from what I know about Coutinho, he is exactly the same.”
Coutinho could play for Liverpool on Saturday when they travel to Manchester City (12.30pm), while Sanchez is in line for a start for Arsenal at home to Bournemouth (3pm).
As for Van Dijk, the defender is still yet to recover from injury sustained earlier this year.
Saints host Watford tomorrow (3pm).