Alonso, 44, is out of work following his sacking from Real Madrid in January but may not be for too much longer.
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Reports have emerged that Chelsea are in contact with the Spaniard as they search for the replacement for Liam Rosenior, but that would be dependent on whether Liverpool stick with Arne Slot.
According to David Ornstein, Liverpool have no intention of parting ways with Slot this summer, and Alonso is not being considered.
Speaking on NBC Sports, he said: "My information is that Xabi Alonso is not under consideration at Liverpool at all and that Liverpool fully intend to go into next season with Arne Slot as their head coach."