Amato, a pounds 4.2m summer signing from Real Mallorca, has apparently become frustrated at his lack of first-team opportunities. Now he may be poised for a move back to Spain as Atletico need cover for the injured pair of Kiko and Fernando Correa.
A club spokeswoman said: "Amato is just one of 20 players on our list. We have to look at all the options and weigh everything up before we come to a decision."
The Spanish striker Pizzi, now playing in Argentina for River Plate, is believed to be the prime target, but Atletico might have to consider another option as they face a compensation claim from his former club, Barcelona, if he returns to Spain.
Atletico's caretaker-manager, Carlos Aquiar, said: "We are about to complete the signing of a striker. Nothing has been confirmed yet but it is close."
Rangers have been in prolific form recently and the 28-year-old Amato was among the substitutes again at the weekend in the 6-1 defeat of Dundee. Rod Wallace, Jonatan Johansson and Stephane Guivarc'h are all being selected ahead of him.
Across Glasgow, the Mark Viduka transfer wrangle is set to rumble on for another three weeks. Fifa, football's world governing body, has requested additional information from Celtic and Croatia Zagreb as well as the Australian football authorities. Fifa has given the three parties until 13 March to supply the documentation required.
Celtic forwarded pounds 900,000 to the Croatian club after a transfer fee of pounds 3m had been agreed. Fergus McCann, the Parkhead managing director, withheld pounds 2.1m to give Viduka's former Australian club their pounds 600,000 share. The player, who has yet to make a first team appearance, is due pounds 1.5m, paid in instalments.
This latest setback has infuriated Zagreb officials, who maintain they should have been paid in full. Their spokesman, Goran Bradic, said: "What can we do? It is ridiculous that Celtic don't want to pay. We are not the guilty party in this situation yet we are continually being punished."
Viduka signed for Celtic before Christmas but then walked out on the club without playing a game, saying he was suffering from emotional stress. He spent Christmas in Australia but reappeared at Parkhead after the after the winter break.
A Fifa spokeswoman said: "The case is still be handled as we need to complete our dossier. The clubs and the Australian authorities have been given a three-week deadline to supply the documentation."
Celtic face Dundee United at Parkhead on Saturday, but Viduka is likely to continue to build up his fitness with the second team.Reuse content