With a holding midfielder still top of Arsene Wenger's wish list, Ivory Coast international Toure would be an ideal replacement for the Milan-bound Mathieu Flamini.
Barca are reported to have already agreed terms with Hleb in regards to his side of the transfer saga, but appear reluctant to include Toure as a makeweight in the deal.
"Nothing has been decided as yet," said Begiristain.
"But we want Yaya to stay with us and he is not on the market.
"(Josep) Guardiola considers him to be an important player in his new project."