The Ghanaian star is targeting a move to a top European club competing in the Champions League, while West Ham would look to prioritise any deal that brings in significant funds to help ease financial pressure and allow new manager Graham Potter to begin reshaping the squad.
A transfer to Saudi Arabia could offer that kind of financial relief, but Kudus is not convinced by the prospect.
With the window now gathering pace, Kudus is emerging as one of the biggest names on the market - but he is waiting to see who makes a decisive move.
In England, Chelsea and Newcastle United have been the furthest along in terms of understanding the situation. Both clubs have assessed the conditions required to sign Kudus, and Chelsea even made a cheeky player swap deal suggestion recently that fell on deaf ears.
Arsenal have also done background work, and while Manchester United looked into the situation earlier in the window, they are unlikely to move forward.
Tottenham Hotspur are expected to explore Kudus as a backup option if other targets fall through. He is one of several names under consideration beyond Antoine Semenyo, Mbeumo and Eberechi Eze. At this point, though, there has been no contact between Spurs and Kudus’s representatives.
West Ham need to sell
West Ham, meanwhile, are privately aware that the 24-year-old wants to leave and are in a financial position where sales are necessary before manager Potter can begin buying new players.
It is understood Kudus had already been thinking about his future before Potter’s arrival - but sources say the change of manager has only strengthened his belief that it is time to move on in order to fulfil his potential.
The player has a release clause set at £85million for Premier League clubs, but within the game there is a general expectation that no English side will meet that valuation.
While West Ham would love to see a Saudi Arabian club come to the table and offer even more money to take him away, the reality is that while such a move would be financially lucrative it would not satisfy the player’s sporting objectives.
The player and his camp have been waiting for firm enquiries to land.

Insiders believe that, privately, the club would eventually be prepared to accept a fee closer to £60 million - provided negotiations and the structure of a deal unfold in the right way.
Newcastle still have Kudus on their shortlist but have not yet placed him at the top of it. Arsenal continue to monitor his situation, with sporting director Andrea Berta known to be considering several attacking profiles. Chelsea, who have long tracked Kudus, may firm up their interest once again as they begin moving pieces in and out of the squad.
For Kudus, the next few weeks are pivotal as he wants to prepare for pre-season with full focus on the game. He seems determined to secure a move that reflects both his talent and ambition.
