Defoe scored his 15th league goal of the season in Saturday's 3-2 win over Chelsea and Allardyce says the 33-year-old would be an ideal replacement for Arsenal's Danny Welbeck, who picked up a knee injury against Manchester City on Sunday.
England face Russia, Slovakia and Wales in Group B of the 24-team European Championship in France, which kicks off on June 10.
"I just think that if Roy needed any striker to go along, Jermain would be his man," Allardyce told British media.
"Jermain's had a big run of games of the sort he hasn't had for a few years, and he's been a consistent performer at the highest level.
"To score 18 goals (in all competitions) for a team that's been sat in the bottom three or four all season is pretty miraculous."
Tottenham Hotspur's Harry Kane (25 goals) and Leicester City's Jamie Vardy (24 goals) are the only Englishmen ahead of Defoe in the Premier League scoring charts.
Defoe has scored five goals in his last eight league games for Sunderland, helping to steer the club to 16th in the table with two matches left.
"Jermain's performance this year and his goals particularly may have caused Roy to just take a little look. He knows how much experience he's got, he knows he can do it at that level," Allardyce said.
Defoe has scored 19 goals in 55 appearances for England with his last cap coming against Chile in November 2013.
