Palestra had appeared destined for Inter after a standout loan season at Cagliari, where he made 34 Serie A starts and was named the division's best defender. Inter had progressed to the stage of presenting personal terms to the Italian international through his agent.
Chelsea then intervened, with David Ornstein reporting the deal is now advancing at rapid pace and an agreement between clubs is expected within 24 hours.
Sources in Italy indicate Inter could not match Chelsea's offer on personal terms, and Palestra is now heavily leaning toward a move to Stamford Bridge.
Alonso, who officially begins work at Chelsea on 1 July, has been in regular contact with the club hierarchy throughout the transfer window. Having been appointed as manager rather than head coach, he is understood to have approved the Palestra deal — making it the first major signing of his tenure and an early signal of his influence over recruitment.
The versatile defender can play on either flank as a wing-back or a conventional full-back. He made his senior international debut for Italy this year.
Chelsea are also pursuing at least one central defender and a midfielder, with multiple sources indicating that a deal for Strasbourg's Valentín Barco is close. A further versatile attacker is also targeted. Several additions will also arrive under deals agreed last year, including £40m winger Geovany Quenda from Sporting CP and Strasbourg striker Emmanuel Emegha.