The 20-year-old has been in excellent form for Leverkusen during the 2019-20 campaign, scoring 15 times and registering eight assists in 38 appearances in all competitions.
The Germany international is currently playing through the middle for his Bundesliga side and has scored five times in his four appearances since the season resumed last month.
Here, Sports Mole looks at the shirt numbers available for Havertz at Old Trafford should he arrive before the end of this summer's transfer window.
Havertz has worn the number 29 shirt since breaking into the Leverkusen first team in 2016 but that jersey is currently occupied by right-back Aaron Wan-Bissaka at Old Trafford.
The attacker has recently sported '7' for Germany, though, and there is a strong chance that number could be available at Ole Gunnar Solskjaer's side during the 2020-21 campaign.
Alexis Sanchez is United's number seven as it stands, but the Chile international, who is currently on loan at Inter Milan, could leave the club permanently during this summer's transfer window.
That said, Jadon Sancho would also surely fancy taking on the famous jersey if he were to arrive at Old Trafford from Borussia Dortmund in the coming months.
Chris Smalling currently has the number 12 for the club, although the centre-back, who is currently on loan at Roma, could leave permanently ahead of next season, potentially opening up another option.
Marcus Rashford's previous number - '19' - is also currently vacant, but it seems probable that Havertz would want a so-called glamorous shirt in order to join the 20-time English champions this summer.