Shakhtar are unhappy with FIFA's decision to amend Annex 7 of the Regulations on the Status and Transfer of Players following the outbreak of war between Russia and Ukraine. The regulation change allows foreign nationals employed in either country to unilaterally suspend their contracts if they wished to leave the region.
Solomon did so to join Fulham last season but the winger still has a year remaining on his Shakhtar contract and is believed to be looking for another club in England.
FIFA recently announced that Annex 7 would be extended through to the summer of 2024, prompting a furious backlash from several clubs affected, who believe they are being unfairly punished in losing revenue through transfer income.
Shakhtar estimate Annex 7 could cost them up to €80 million in lost transfer fees if players like Solomon are allowed to leave for nothing.
Although the Court of Arbitration for Sport upheld FIFA's original decision, Shakhtar are now preparing a case at the Swiss Federal Tribunal and have also lodged an appeal with the European Commission.
Palkin warned Spurs they will also face legal action if they attempt to exploit the situation to their advantage.
"I contacted Solomon and his agent and invited him back to our club," Palkin told ESPN. "I said 'you can play all the games in Champions League, you will be in the starting eleven' but he doesn't want to move and I believe he will stay in England.
"Finally, where he will go, I don't know. In any case, if you go to Tottenham, we will deal with Tottenham in court in this case. Everything comes to a simple situation: it sounds like unjust enrichment.
"Can you imagine, we pay big money for this player and finally Tottenham receives him for free? It is not fair in respect of our club. We will definitely go to court and we will fight for ourselves."
Palkin extended that warning to any club planning to sign Shakhtar's players with the help of Annex 7 this summer.
"I would like to send a message to those clubs who are trying to sign our players without paying a transfer fee: Shakhtar will file claims for unjust enrichment against players or clubs who have enriched themselves and benefitted by obtaining a financial advantage," he continued.
"We believe these clubs who enrich themselves at Shakhtar's expense will be obliged to pay restitutions. Those clubs should understand what they do when they decide to sign our players."
Palkin also negotiated the €100m transfer of winger Mykhailo Mudryk to Chelsea in January. The west London club beat off competition from Arsenal for the 22-year-old, but Mudryk has so far struggled to produce his best form in England, registering two assists and failing to score in his 17 appearances for Chelsea.
However, Palkin backed the Ukraine winger to thrive under new Chelsea head coach Mauricio Pochettino after a dismal campaign in which the team finished 12th in the Premier League, losing 16 matches.
"First of all, I'm not in a position to criticise him," Palkin said. "If, for example, the whole of Chelsea was in a good way and just Mudryk arrived and showed very bad football, it is one story.
"But I think today Chelsea is on the way to build a new club, a new team, to invite a new coach and they are in the beginning of a new era of Chelsea.
"Therefore, Mudryk is a major weapon for Chelsea to win future titles. When the new coach arrives and sees Mudryk, pays attention to Mudryk, I believe 100% he will give the full fee back and show unbelievable football.
"I know him from 15, 16 years old. I know what kind of player he is and what kind of football he can show. At this moment, it is quite difficult. On one side, €100m is some kind of pressure and he wants to show something but when you want to do that, sometimes you can show nothing. From a mental point of view, you need to be calm, train and show his football together with his team.
"He should grow together with his coach. I believe he will show very good football. He needs just time."