Alan Nixon of the Sun reported on Monday that the American stopper wants a four-year deal worth more than £14 million to join the MLS team.
Nixon noted the Rapids are "shocked" by the United States No. 1's demands and that negotiations are "dragging" as a result.
Howard moved from MLS to England in 2003 after a high-profile switch from the MetroStars to Manchester United, where he spent four seasons.
He spent his last year with United on loan at Everton after falling out of favour with then-Red Devils coach Sir Alex Ferguson, and Howard has remained in Merseyside since.
The goalkeeper became a cult hero for United States Men's National Team fans at the 2014 World Cup, where Howard's heroics were celebrated as the team made the knockout rounds.
The stopper currently has two years left on his deal with the Toffees, according to Nixon, and is currently due £70,000 per week.
Howard desires his wages at the Rapids to remain in line with his current earnings but wants a four-year commitment from Colorado despite being a veteran of 36.
Rapids blogger John Patrick Rosch from SB Nation's Burgundy Wave was not impressed with the size of the reported deal. He wrote:
If this is to be believed, and this is a big if, that is way too much for a goalkeeper. Yes, Howard is a great goalkeeper and all, but that is just too much. Getting Howard in Colorado would be a great coup for the team, but that is not their greatest area of need. And nearly 20 million is a tough pill to swallow.
Rapids, if this is true....run away. Run away fast.
Howard's tenure in the Premier League has long been admired by football fans from the United States, but his form for Everton does not suggest he is worth the investment.
The quality in MLS has risen in recent years, and Howard would find it impossible to find a similar deal in England, making him a less valuable asset for any purchasing club.