Eberechi Eze is the only arrival to have set the club back a transfer fee so far, but with budgets restricted by coronavirus, sales may need to fund any more spending.
Alexander Sortloth is set to join RB Leipzig for £20million — with the fee to be split separately with Trabzonspor after his loan was cut short — while they would listen to offers for Connor Wickham and Mamadou Sakho among others. Wilfried Zaha could still leave, though there has been no interest in the 27-year-old so far.
“Funds are always of crucial importance, so I don’t think there is a simple answer to that problem,” Hodgson said ahead of Saturday’s trip to Manchester United. “To get the quality of player that I would think we would need would require funds, and whether those funds would be available without someone being sold, I don’t know at the moment.
“We’ve had targets all through the window. I will have to wait and see if the club has the funds to bring those players in if we can persuade those players to come.”
While a striker remains a priority, there could be another addition at the back in Nathaniel Clyne, who has returned to train with his former club in a bid to regain fitness and a contract.
Clyne is a free agent, having been released by Liverpool, and Hodgson is weighing up whether to bring in his former England right-back as injury cover for Nathan Ferguson.