According to Sport Bild, Hamburg are already assessing potential additions for the second half of the season, with their plans extending beyond short-term reinforcements.
The Bundesliga club are particularly interested in loan agreements that include an option to make the transfer permanent, allowing them to strengthen the squad immediately while retaining flexibility over longer-term commitments.
Grönbaek's arrival has provided an example of how that approach can work.
The Danish midfielder joined Hamburg on loan from Rennes in the winter of 2025, with the agreement including an option to buy.
He quickly established himself as an important member of the team, impressing in an attacking midfield role and becoming a regular contributor.
His performances convinced Hamburg to make the move permanent during the summer, with the club paying €4.7 million to secure his services.
That deal has now become a reference point for the club as they look towards the next transfer window.
Hamburg are keen to identify similar opportunities, particularly players who can make an immediate impact without requiring a significant upfront commitment.
The loan-with-option structure would also allow the club to assess how potential recruits adapt to the Bundesliga before deciding whether to invest in them permanently.
With the January window approaching, Hamburg's recruitment team will continue to examine the market for players who fit that profile. Grönbaek's progress has demonstrated the potential benefits of the strategy, and the club could look to repeat the formula in the months ahead.