But Spurs have declined, saying it would remove the incentive for UEFA to “price sensibly in the future”.
Liverpool have not yet responded to the supporters’ suggestion.
SOS and THST also asked the clubs to extend season ticket payment deadlines to allow fans time for another pay-day after the final, which Tottenham have agreed to.
The Champions League final takes place at Estadio Metropolitano in Madrid on Saturday 1 June at 20:00 BST.
Significant costs for fans
It said of the club’s 16,000 allocation, 6,500 were not for general sale, and Reds’ fans would get 3,000 fewer tickets than Spurs.
Liverpool’s season ticket payment deadline is currently 24 May, a week before the final.
The club said it hoped future competitions “can be priced more reasonably and made more widely accessible”.
It added: “For the game in hand however we do not feel it is appropriate for us to subsidise ticket prices, not least because it would remove any incentive for competition organisers to price sensibly in the future.”
THST said it did not agree that “using income made from the clubs’ runs in the competition to subsidise tickets would remove the incentive to reduce prices in future” but it was happy the club had “acknowledged the significant costs to our fans”.
“We are happy that it is pressing the issues of pricing and allocation with UEFA. When clubs and fans work together, we can secure change,” a spokesman added.