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A report suggests Bournemouth, Chelsea and Watford may not fulfil a pledge to meet standards by August 2017.
It stressed clubs have been "working hard on delivery" since a 2014 BBC report found that 17 of 20 clubs did not provide enough wheelchair spaces.
But campaigners have criticised the failure to meet the standards set out.
"The time for excuses is over," said David Isaac, chair of the Equality and Human Rights Commission.
"The Premier League promised that disabled access would be improved by the start of next season, so it is disappointing that a number of clubs will fail to meet that deadline.
"Clubs need to urgently demonstrate to us what they are doing to ensure they are compliant with the law and how they are making it easier for disabled fans to attend matches. If they don't they will face legal action."
The Premier League's report comes after MPs argued last month that top-flight clubs were prioritising finance over improving access and meeting the Accessible Stadia Guidelines.
The Culture, Media and Sport select committee report said clubs should face legal action if they fail to meet the basic needs of disabled fans.
The Premier League board can impose fines of up to £25,000, while cases of serious breaches would be referred to an independent panel - which could impose heavier fines or even deduct points.
Bournemouth have 195 disabled fan spaces but not to the required standard. However, they do not own their Vitality Stadium home and the club says that the stadium's small size makes meeting guidelines difficult. It is planning to move to a bigger ground in the coming years.
Chelsea have 128 spaces for disabled fans, against a recommended 214. The club is aiming to move to a new 60,000-seat stadium and says in the meantime it will consult with disabled fans.
Watford have spaces for 61 disabled fans, but should provide 153. It will have more wheelchair spaces by August but says it faces architectural challenges and is aiming to make other improvements to boost the matchday experience of disabled fans.
Burnley, Middlesbrough and Hull were given extensions to 2018 to meet the guideline standards as they were only promoted last summer.
"Premier League clubs have embarked on a substantial programme of work and rapid progress has been made. The improvements undertaken are unprecedented in scope, scale and timing by any group of sports grounds or other entertainment venues in the UK.
"Given the differing ages and nature of stadia, some clubs have, and continue to face, significant challenges. For those clubs, cost is not a determining factor.
"They are working through issues relating to planning, how to deal with new stadium development plans, how to best manage fan disruption or, in cases where clubs don't own their own grounds, dealing with third parties.
"Clubs deserve credit for committing to and delivering the extensive work detailed in this interim report. What is also clear is that even more progress will be achieved in creating the appropriate levels of access for disabled football fans by our own deadline of August 2017.
"Beyond that date, clubs will continue to engage with their disabled fans and enhance their provisions in the coming months, years and beyond."
2014: A BBC investigation finds that 17 of the 20 clubs in the top flight at that time had failed to provide enough wheelchair spaces.
September 2015: The Premier League promises to improve stadium facilities for disabled fans, stating that clubs would comply with official guidance by August 2017.
September 2016: Campaigners say up to a third of clubs will miss the deadline to meet basic access standards.
October 2016: Leading disability campaigner Lord Holmes tells MPs that legal action against clubs and the Premier League remains an option if standards are not met.
January 2017: A report by MPs says some clubs could face sanctions because they are not doing enough. Manchester United, Liverpool and Everton announce plans to develop their grounds to accommodate more disabled supporters.
1 February 2017: A Premier League report outlines the detailed work the clubs are undertaking to make sure they meet guidelines but adds that three clubs will miss the August 2017 target.
At least three clubs are at risk of missing a self-imposed deadline to improve access for disabled fans, the Premier League has said.