The 20-year-old is set to sign a four-year contract with an option for a fifth season should the transfer be finalised. The two clubs are currently negotiating the remaining details, principally the sell-on clause percentage, with Lazio seeking to keep that figure as low as possible.
The relatively modest initial fee reflects Asp Jensen's profile as a developing talent rather than an established first-team player, and the sell-on clause negotiation suggests Bayern are keen to retain a share of any future profit on a player they believe has significant upside.
Whether the two clubs can agree on the sell-on percentage will determine how quickly the deal moves from an agreed framework to a completed transfer. The player's own position is clear — he has already signalled his willingness to move to Rome and take the next step in his development in Serie A.
Lazio's pursuit of Asp Jensen fits the club's stated summer philosophy of targeting young players with growth potential rather than established stars, which head coach Gennaro Gattuso and president Claudio Lotito have both outlined as the guiding principle for their transfer activity this window.
The four-year contract length with an option for a fifth year gives Lazio significant commitment to the player while protecting their investment. For a club working within financial constraints and a transfer market block, recruiting young talent with a structured deal of this kind is consistent with how they have approached other business this summer.
Bayern Munich, for their part, have a decision to make about whether €4m adequately reflects Asp Jensen's value and whether the sell-on structure proposed by Lazio gives them sufficient participation in the player's future earnings. Both elements will need to satisfy the German club before the deal is finalised.