LaLiga champions Madrid are prepared to pay around €80 million to land Tchouameni, who joined Monaco for €20m from Bordeaux in 2020.
However, the Spanish treasury considers the Principality of Monaco a tax haven and are therefore expected to demand Monaco pay 24% in taxes on top of the €60m profit they stand to make from the deal.
Sources close to the negotiations have told ESPN that the Ligue 1 club hope Madrid will pay the additional money, which is just under €15m, but the Spanish side are resistant to doing so.
A source close to Tchouameni played down the issue, saying everything is progressing "as expected" and that they expect the move to be completed next week.
It is not a new situation for Monaco. They have previously been forced to pay tax on profit from player sales to Spanish clubs, including on the transfers of James Rodriguez, Yannick Carrasco and Aymen Abdennour, and are keen not to be stung again.
They will fight against tax on profits from sales into the Spanish market, and until there is legislation in place that supports their argument, they are not prepared to take any risks.
Various sources don't believe the hurdle will be detrimental to the deal, though, with Tchouameni turning down several other clubs, including Liverpool and Paris Saint-Germain, to push through a move to Madrid.
ESPN revealed on Tuesday that Madrid are close to signing him on a five-year contract and are now working on the final details of an agreement worth around €80m with Monaco.
Madrid have been following Tchouameni for several years but stepped up their interest in January with the idea of completing a deal this summer.
President Florentino Perez is moving ahead with plans to rejuvenate the club's midfield after missing out on Kylian Mbappe, who renewed his contract with PSG until 2025 last weekend.
Tchouameni, 22, will join Eduardo Camavinga, who signed for Madrid last summer from Rennes, and Federico Valverde in putting pressure on the current trio of Casemiro, Toni Kroos and Luka Modric, who are all in their 30s.
Information from ESPN's Sam Marsden was used in this report.