If West Ham do make the transfer it will be an interesting move, as Pellegrini has previously commented on Costa before and it was not all positive.
After Costa was sent off when playing for Chelsea against Liverpool for a stamp, Pellegrini said: "He is a great player, a very important player.
"He has his character, it is not an easy character, but I hope for him that (with) this punishment - and I am not trying to take advantage for the game tomorrow - it will be a good thing for him to change in the future because he doesn't need to do it in that way because he is a very good player, a top player."
Costa’s disciplinary problems still have not been eradicated out of his game, and at the age of 30, it seems unlikely that he will ever change his attitude on the pitch.
Pellegrini may be willing to make an exception for Costa’s angry flashes though, as West Ham do currently need a striker.
The Hammers have sold Marko Arnautovic this summer, meaning they are short of numbers up top.
It doesn’t seem like Costa is a leading candidate to be signed by West Ham at this stage, but he could be a possible option if they fail to land other targets.
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