An application for a temporary 25-metre tower has been submitted to Rushmoor Council by Hutchison 3G UK Ltd.
Hutchison says this would be a short-term solution while it makes arrangements to share a mast at the ground used by Orange and BTO2.
Tracy Holman, of Peach Tree Close, is among several concerned residents.
She said: "Our main cause is the health implications, particularly as there are two schools close by and children are going to be walking past every day.
"I'm also worried about parking on match days, which is already a nightmare. If they're putting up another phone mast it will only take up more space."
The company has sent letters and a copy of the plans to Grange Community Junior School and Farnborough Grange Infant and Nursery School.
But the school holidays mean many parents are away and will miss the comment deadline on August 22.
Two years ago the government commissioned a study of electromagnetic emissions from phone masts, the findings of which were published by the Radiocommunications Agency earlier this year.
The first results showed the levels of emissions from masts near 100 schools were well below the guidelines set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP).
Hutchison says the football ground site's emmissions would still be within ICNIRP levels even if a second mast was added — but many people remain unconvinced that phone masts do not harm people.
Grange ward councillor Mike Smith is backing the residents, saying: "It's all very well the government issuing guidelines about the safety of phone masts but it remains to be seen what the long-term effects are.
"Everyone used to say that smoking was good for you but they turned out to be very wrong, and I just hope that the same mistakes are not made with phone radiation."
And Karen Bigwood, also of Peach Tree Close, added: "There is no specified date when the mast will be removed and this leaves the application open to abuse.
"The current mast dominates the local skyline and I fear that if they let another one go ahead we could soon have a colony of towers."
Rushmoor's development control committee will look at the application on September 4.