Gaston Ramirez has handed in a transfer request at Middlesbrough
The Premier League champions have had one offer for the 26-year-old turned down but Ramirez has handed in a transfer request to force a move to the King Power Stadium.
Leicester manager Claudio Ranieri said: "It is important to add to the squad.
Claudio Ranieri wants to add to his Leicester squad
But Middlesbrough boss Aitor Karanka questioned Ramirez's ambition but went on to say anybody in his squad can be replaced.
"It's a step for him to maybe play in the Champions League this season. He can think about that," said Karanka.
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"I can't think it's a big move for him in the future. The club knows (his value), I'm not going to say. If one player isn't happy here, he can leave with the right offer.
"If it's not enough for us, maybe I'll have three or four players knocking on my door, everyone has his value."