William Hague, who was foreign secretary until last year and is still a minister seen as close to Prime Minister David Cameron, said governments should think "very, very carefully" about such a move.
Foreign Secretary Philip Hammond said earlier this month that, while Britain was not currently planning to supply "lethal aid" to Ukraine, "we reserve the right to keep this position under review".
Britain is already sending non-lethal equipment such as light armoured personnel carriers to Ukraine.
He stressed that a "diplomatic solution" was the way forward and warned: "You have to think very, very carefully" before sending in additional arms to a conflict.
Opponents of sending arms have argued that it could result in a proxy war between Russia and the West.
US President Barack Obama said this month that he had not yet made a decision on whether to send weapons to Ukraine, where Kiev's forces are pitched against pro-Russian separatists.
Russia's repeated denials that it is providing military backing for the separatists have been dismissed by the West.
