Sport reported that Los Merengues lodged a new €35million bid for the former Real Sociedad star, and the Reds have already accepted it.
At the early stages of the negotiations, Liverpool put a €38million price tag on Alonso's head, while Real only offered €27million, before meeting the Premiership side halfway.
"He (Alonso) would be very good for us because he would bring balance," Real sporting director Miguel Pardeza commented on the anticipated swoop.
"The transfer market has turned the creative midfielders into an extinct species. The very few who are left are either highly valuable or impossible to prise away from their clubs.
"We're not signing him just for the sake of signing him. I wish there were more alternatives to Xabi, but the market does not offer any."
Spain ace Alonso reportedly took no part in Liverpool's Wednesday friendly with Thailand, which ended in 1-1 draw, because his club were keen to avoid the risk that he could get injured and halt the deal.
No Guarantees
From his side, the 27-year-old assured that his future is still far from certain.
"It's difficult to give any guarantees," Alonso told Daily Mirror.
"For now, I'm just enjoying myself in Thailand."
نرشح لكم
حوار في الجول - جونينيو: هذه مشكلة الجيل الحالي للبرازيل.. ومرموش يسير على خطى صلاح
عودة العلاقات؟ BBC: صلاح يعود لقائمة ليفربول لمواجهة برايتون
مؤتمر فليك: ريال مدريد لم يفقد المنافسة.. ولن أتحدث عن ألونسو
مستقبله على المحك.. أس: 3 مباريات حاسمة لمستقبل ألونسو
للمرة الأولى.. إيجور تياجو أفضل لاعب في شهر نوفمبر بـ الدوري الإنجليزي
"سأكون كاذبا إذا رفضت".. بنزيمة يفتح باب العودة لمنتخب فرنسا
مؤتمر سلوت: سعيد بتوديع كأس الرابطة الإنجليزية.. وهذا الثنائي يغيب لأسابيع
فرصة شوبير؟ ليفاكوفيتش يرفض المشاركة مع جيرونا من أجل الرحيل












هشام نصر: سنرسل خطابا لرئيس الجمهورية لشرح أبعاد أرض أكتوبر