Rossoneri owner Silvio Berlusconi's Sport Mediaset reported on Tuesday that the two clubs were negotiating a season-long switch with a view to a permanent deal worth around €17 million [£13.5m].
However, being on the verge of securing the arrival of forward Bojan Krkic, Milan CEO Adriano Galliani told reporters: "I continue to say it, but you do not believe me, with the signing of Bojan the market is closed, completely closed.
"[There will be] no trip to Madrid for Kaka, nor any signings like [Antonio] Nocerino last year. He [Palombo] was offered to us, but we refused the offer.
"Carroll? We have so many strikers."
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Carroll's future has been the subject of much speculation since new boss Brendan Rodgers arrived at Anfield in the summer but Milan's captures of Giampaolo Pazzini, M'baye Niang and the imminent Bojan appear to have filled the void left by Paris Saint-Germain-bound Zlatan Ibrahimovic.
In recent months both West Ham and Newcastle have also expressed an interest in Carroll, who has failed to find his best form since arriving at Anfield for £35m in January last year.