The commission said the University of Southampton was keen to look into biofuels, arguing it was time to "move the debate forward".
But the last time a group of scientists tried to plant trees in this country - in Bracknell, Berkshire, nine years ago - activists destroyed more than 100 specimens.
The Southampton team reckons GM poplars with reduced amounts of lignin may be easier to convert into the biofuel ethanol.
A representative for the university said: "Work in this area is very highly regulated and the researchers will be seeking the relevant permissions.
"Although this proposed work is still in the very early planning stages and no GM trees have been planted, we feel the research could have significant potential."
But Friends of the Earth said lignin protected trees against pests and diseases, and argued that cross-contamination could blight the world tree population.
Anti-GM campaigner Clare Oxborrow added: "The concerns are massive: trees live long and spread pollen over large distances."
She added: "It may seem a big leap from Southampton to South Americans who depend on forest ecosystems. But the direction of research will have an impact on other countries."
A Forestry Commission representative said: "We are considering (the University of Southampton's) request. There is no timescale, no sites have been identified and it all needs Defra approval."
Defra said it had received no notification of the research plans, which are led by Professor Gail Taylor at the university's plant and environment lab.
Her web page says "functional genomics" can answer big ecological questions and smaller-scale ones, such as what determines the size and shape of a leaf.