Nolan is not bothered about missing out on those signings, however, and he insists anyone who comes in over the next fortnight must be fully committed to dragging West Ham out of the relegation zone.
"We don't want those players (who turned us down), simple as," Nolan said.
"I don't want to play with a player who gets his head turned easily or doesn't fancy the challenge.
"We only want players who are going to go out there and put their hand on their heart and say: "I am here for the club". We want them to be here. If you don't want to be here then don't bother."
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