The Ukraine striker has endured two disappointing years at Stamford Bridge following a big-money move from Milan.
Reports suggest Shevchenko could return to Milan in what would initially be a season-long loan deal following a meeting between former club president Silvio Berlusconi and Chelsea owner Roman Abramovich in Sardinia last Thursday.
The Italian press claim the deal will be finalised on Thursday or at the latest 24 hours later and Ramaccioni agrees.
"Shevchenko in the Rossoneri shirt? There really isn't much more to be done," he told Radio Goal.
"We are close to the end of the deal and I hope that these little things that have to be fulfilled are done as soon as possible.
"I would be extremely delighted if Shevchenko returns to Milan and I am ready to embrace the Ukraine champion again, for us it's about a return home."