The Spanish manager previously worked closely with the Germany international during their highly successful time together at Bundesliga side Bayer Leverkusen.
Wirtz earned a massive £116 million transfer to Anfield last summer off the back of his brilliant performances under Alonso.
The 23 year-old attacker has struggled to consistently find his best form in English football since making the high-profile switch to Merseyside.
The Germany international registered seven goals and ten assists across 49 appearances in all competitions during his debut campaign in England.
Speculation regarding a potential reunion became intense after the 44 year-old manager accepted his first managerial appointment in the Premier League with Chelsea.
Media reports claimed the west London club were actively keeping tabs on the player as a potential replacement for midfielder Enzo Fernandez this summer.
Club sources have completely rubbished those claims, stating there is absolutely no truth to the rumors linking the player with a move to London.
The Blues hierarchy are targeting at least two new first-team signings to significantly bolster the squad ahead of the upcoming campaign.
Club officials have also dismissed recent links to several other high-profile targets including Manchester City defender John Stones and Arsenal youngster Ethan Nwaneri.
The recruitment team is working to identify realistic alternatives who fit the specific tactical profile required by the incoming Spanish manager.
Wirtz looks set to remain at Anfield to prove his worth under their own new management structure rather than forcing an exit.
Alonso will focus his immediate attention on assessing his inherited squad before finalising any major transfer additions before the deadline.
The London club will prioritize structural reinforcements elsewhere on the pitch rather than pursuing another expensive attacking midfielder this summer.