Palkin says discussions took place between Shakhtar and Spurs when Solomon initially moved to north London, with both clubs agreeing that Spurs would part with a fraction of any future sale.
"We had arguments and discussions with Tottenham,” Palkin said.
"Verbally, we agreed that when they sell the player, they will pay us part of the sale. Now we will come to them officially with our suggestions and our view of the situation.
"If we have problems in these discussions and negotiations, we will go to some intermediaries."
Manor Solomon joined West Ham from Tottenham in the summer
Getty
Palkin added that he hoped Shakhtar and Spurs could come to an amicable arrangement, but admitted he was open to taking the case to the European Club Association or Cas (Court of Arbitration for Sport) if a deal could not be struck.
"If they are friendly and we agree, then this issue is closed. It's better to do it in a friendly way."
Spurs have been contacted for comment.