The Spaniard switched Merseyside for Madrid in 2009, but has repeatedly been linked with a return to his old stomping ground.
The Daily Star's Jack Wilson has told that Real are uncertain whether their playmaker will be signing a new contract, but goes on to add that the matter should be solved in the next "two to three weeks."
Tancredi Palmeri of CNN has quotes from Carlo Ancelotti concerning his player's situation:
An excerpt from Wilson's report reads:
David Moyes is keen to bolster his midfield and pass-master Alonso would be an experienced option to replace Paul Scholes.
Alonso's Premier League credentials need no testimony, the 32-year-old having finished as runner-up in the 2008/09 season, as well as winning the Champions League, FA Cup and UEFA Super Cup during his time with the Reds.
Since moving, however, Alonso has only matured further, and in the best-case scenario for Liverpool, could be what Andrea Pirlo is to Juventus or, as Moyes would have it, what Paul Scholes was to Manchester United.
Admittedly, Alonso would be a fairly short-term solution for the Merseyside outfit. At 32, he's only two years younger than Brendan Rodgers' current midfield general Steven Gerrard, but the most important thing is that the veteran possesses quality, which is what Liverpool need above all else right now.
As they seek to get back into contention as one of the Premier League's biggest clubs, the Reds should be trying to do away with the quantity-over-quality approach that has led to their downward slope of the last six years or so.
Even if Alonso were to be looked upon as a two- to three-year option, that's at last two to three seasons in which the club can rest safe in the knowledge that their midfield is anchored by a consistent and reliable resource.
Though Alonso's not the flashiest of Real's players, OptaJose tweeted to show exactly how essential Alonso's influence is at the Bernabeu:
Aside from what he would bring onto the pitch, Alonso's return would be as much of a morale boost as anything else, a sign that the club are indeed capable of drawing in the world's biggest talents, albeit having a slight advantage in this scenario.
If Europe is once again to be convinced of Liverpool's return as a continental force, it's deals such as these that they must be competing in, and are right to do so.
Alonso's return to Anfield would be a coming-full-circle moment for Rodgers' squad, one of the greatest heroes from a time gone past coming back to help shape the club for future years to come.