Shrewsbury Town Council has confirmed it has submitted a planning application to Shropshire Council to fell the lime tree, which is situated next to the entrance of the Quarry park off St Chad's Terrace.
In a statement the council said: "The Lime tree is in poor condition showing signs of significant decline in vitality with poor shoot extension and die back in the crown.
"This has resulted in a small live crown. The tree also has substantial decay in the lower stem and buttress."
The statement added: "We appreciate that it is in a Conservation Area, but despite our best efforts, the tree is in a poor condition and showing signs of significant decline."
Shropshire Council will take a decision on the application.