Other suggestions put forward by Gartside including having a two-tier Premier League will be fed into the league's ongoing strategic review.
The Premier League said in a statement: "Bolton Wanderers submitted a discussion paper detailing ideas concerning the restructuring of the Premier League into two tiers with the inclusion of Celtic and Rangers.
"The clubs welcomed the additional input into an ongoing process, however, they were of the opinion that bringing Celtic and Rangers into any form of Premier League set-up was not desirable or viable.
"The other relevant ideas contained within Bolton's paper will now be taken forward as part of the wider strategic review being undertaken by the Premier League since November 2008 with the aim of providing recommendations before December 2010."
Gartside has expressed concerns that too much money continues to flow into the coffers of the top four clubs.
Last season, champions Manchester United earned £52.3million in Premier League television money, compared to £31.6million for bottom club West Brom.
The fact that the four clubs in the Champions League also earned between £20million and £33million on top of that from European TV and prize money - and benefit from huge ticket and merchandise revenue - has led to a number of chairmen of mid and lower-ranking clubs to believe the time has come for a review.
In his annual report, published last week, Gartside made it clear that he believed addressing the big differences in income was the league's greatest challenge.
Gartside said: "Addressing this polarisation of clubs and the increasing revenue differentials will, I believe, be the major strategic issue for the Premier League over coming years.
"The Premier League is an exciting product for supporters and for television viewers, but there is no doubt that as the years go by, and the same few clubs continue to benefit from the huge additional revenues from the Champions League, the remaining clubs find it enormously difficult to challenge.
"At the same time, the gap between Premier League revenues and those of the Championship continues to widen and I believe a 'fear factor' is beginning to emerge amongst Premier League clubs outside the top few."
The big clubs will oppose any major change to the status quo pointing out they have already boosted income to the smaller clubs by agreeing to every club receiving payment of facility fees for at least 10 televised matches totalling £4.8million, even if they only appear in a handful of live games on TV.
The next overseas TV deal - which is split equally among clubs - is likely to be close to £1billion, almost twice as much as the current £650million, meaning an extra £6million per club per season.