No, it is highly unlikely that any prominent football teams use a pitch that is close to square in shape.
On page 7 of the 2015/16 FIFA Laws of the Game it states:
The length of the touch line must be greater than the length of the goal line.
This means that it is theoretically possible for a football field to be close to square (eg. 89m x 91m).
However, most clubs will try to construct a field as close as possible to international sizing to provide a consistent experience for players and spectators:
- minimum 100 m (110 yds)
- maximum 110 m (120 yds)
- minimum 64 m (70 yds)
- maximum 75 m (80 yds)
Many football associations will not allow clubs to participate in competitions with a field with dimensions that greatly differ from international sizes.
The FA, for example, for football clubs in England, suggests the following dimensions (which correspond to the minimum international size) in The FA Guide to Pitch and Goalpost Dimensions (pdf link) on page 3 (quoted from a table):
The FA Recommended Pitch Sizes
Over 18 (senior ages) (Age grouping)
11 v 11 (Type)
110 x 70 (Recommended size without runoff (safety area around pitch))
(Length x width (yards))
Many higher-level leagues have a number of criteria for entry aside from first-team performance, and one such criterion is ground facilities. This criterion includes not only dressing rooms, lighting and spectator seating, but also the quality of the field. A field with dimensions completely inconsistent with others in the league is likely to be seen as inadequate.
The reason that such a large range of sizes are still allowed, is that football is played in a variety of locations - some in which the land is not readily available to construct an international-sized pitch.
It may be possible to find a nearly-square pitch in recreational leagues in developing nations, but once a club has reached a semi-professional league (ie. a league in which some players receive some remuneration, but not enough to derive a steady income) it will have a pitch with dimensions that are very close to, if not consistent with an international-sized pitch.