Spurs signed Solomon on a free transfer this summer due to a ruling from FIFA which allows foreign players to terminate their contract with any Russian or Ukrainian club for nothing due to the war between the two countries.
Solomon moved on loan to Fulham in the summer of 2022 after the ruling had come into place, with Shakhtar not receiving a loan fee.
The ruling has been heavily condemned by Ukraine's big clubs, who claim that they are missing out on millions in potential income, and therefore causing debt to rack up.
Palkin in particular expressed his fury at FIFA's decision to implement this rule, saying to ESPN: "Clubs sign our players for whom we paid millions of dollars or euros but nobody helps us. At the same time, FIFA push us to pay back all our debts.
Palkin continued: "Since the war started, I have up to €40million in debt. This is debt for players who were released by FIFA and at the same time, I cannot sell players, I cannot loan players but, at the same time, I need to generate money for players. It is a ridiculous situation."
Chelsea's move for Mykhaylo Mudryk did not fall in line with his ruling, given that he himself is Ukrainian, but Shakhtar have lost players such as Tete, Marlon and Solomon for nothing this summer.
Palkin is also keen to stress that all he wants is the £6.5m the club paid Maccabi Petach Tikva for Solomon in 2019, and that it is not a manoeuvre to make money.
The chief exec stated: "For Tottenham, it is not big money. We paid £6.5million and I don't believe this is huge money for a club of Tottenham's level, for a club that participates in the Premier League. I believe it is possible to cover these losses. I am not trying to generate some kind of profit."
Spurs' Director of Football Administration and Governance Rebecca Caplehorn has agreed that the club will send a proposal to Shakhtar, according to Palkin.
Palkin confirmed: "We had conversations with Tottenham, with Rebecca, We agreed she will send propositions. We are now in, let's say, a negotiation process with them."
The Israeli international has featured in all but two of Tottenham's matches this season, also earning starts against Sheffield United and Burnley in the Premier League.
Solomon also showed bright sparks at Fulham on loan last season, scoring five goals for the Cottagers, who comfortably stayed up in their first season back in the Premier League.