Alonso has been heavily linked with a move out of Anfield again this summer with some reports suggesting a switch to Real Madrid has already been agreed.
Liverpool boss Rafa Benitez insists he wants the 27-year-old to stay after a fine season for the Reds but continued speculation over his future suggests another summer of uncertainty.
He has also been linked with a move to Arsenal and Fabregas would be delighted to team up with his fellow countryman at the Emirates next season.
He said: "Xabi would be great. He's experienced and can score goals. I'm sure the boss is aware of that fact.
"We have lost big players, but the boss knows what he is doing.
"The days of signing a new player aren't finished.
"We need someone in the middle to make competition and make a difference, plus give us a new dimension.
"I think that is all we need. The rest is perfect."
Arsenal last week