Alonso's men, who have a Europa League final against Atalanta and a German Cup final versus Kaiserslautern to come this week, have not lost in any competition this season -- a run of 51 games.
Bayern Munich coach Thomas Tuchel confirmed on Friday he will leave the club at the end of the season, saying he "couldn't agree on terms" to stay on.
Bayer Leverkusen stretched their season-long unbeaten run to 50 games with a 5-0 win at 10-man Bochum on Sunday.
Xabi Alonso's rampaging Bayer Leverkusen will have an additional incentive in Thursday's home second-leg Europa League semifinal against Roma: breaking a 59-year-old European football record.
Bayern, who are in second place on 69 points, two ahead of Stuttgart in third with two games left, face Real in Spain on Wednesday after their 2-2 draw in Munich.
Harry Kane has his eyes set on Robert Lewandowski's record for most Bundesliga goals in a season after scoring twice in a 2-1 victory over Eintracht Frankfurt, but the England striker acknowledges he needs "to get a move on".
Leverkusen have now scored 16 goals in stoppage time in all competitions this season
Honorary Bayern Munich president Uli Hoeness said it would be "a catastrophe" for Julian Nagelsmann if Germany are not successful at Euro 2024 after turning down the chance to return to his club.
Bayern Munich coach Thomas Tuchel said forward Serge Gnabry "will play and will score" in Tuesday's Champions League semi-final first leg at home to Real Madrid, but Leroy Sane's status for the match is in doubt.
With 24 wins and four draws in the league this season, Leverkusen are on the cusp of going through a Bundesliga season undefeated.
Bayern Munich's Bundesliga title hopes all but evaporated following a 2-0 home loss to Borussia Dortmund on Saturday that left them 13 points behind leaders Bayer Leverkusen with seven games remaining.
Bayern Munich forward Harry Kane said he is enjoying every moment as he aims to break more records in Germany after scoring a record setting hat-trick in Bayern's 8-1 thrashing of Mainz 05 on Saturday.
Kane now has 30 goals in his first season in Munich colours, matched the record for a maiden campaign set by Uwe Seeler for Hamburg in 1963-64
Serhou Guirassy scored his 21st goal of the season as Stuttgart beat 10-man Union Berlin 2-0 on Friday to move one point behind second-placed Bayern Munich in the Bundesliga.
Xabi Alonso has taken Bayer Leverkusen to the brink of their first Bundesliga title, but the rising star of European coaching could soon be on the move to Liverpool or Bayern Munich.
Bayern Munich must follow their 2-1 victory over RB Leipzig with a winning run to get their season back on track, forward Harry Kane said.
Outgoing Bayern Munich coach Thomas Tuchel joked "my bag is packed" after watching his side's 2-1 win over RB Leipzig while sitting on a silver-coloured suitcase on Saturday.
Xabi Alonso said on Friday links to Liverpool and Bayern Munich were "just speculation" and that his "head is here" as he strives to take his record-breaking Bayer Leverkusen side to a first Bundesliga title.
A long-range shot from Robert Andrich took Bundesliga leaders Bayer Leverkusen to a 2-1 home win against Mainz on Friday, setting a new German record of 33 games unbeaten.