Bamford bagged his 15th goal of a superb Premier League season in Saturday's 3-1 victory at home to Tottenham Hotspur in front of Three Lions boss Gareth Southgate who looked on from the Elland Road stands.
Tottenham's Harry Kane and Everton's Dominic Calvert-Lewin are the league's only English players to have outscored Bamford this term but the Whites no 9 has still yet to be handed any call up into Southgate's squad.
The European Championships will start in exactly one month's time, and Bamford says he will keep trying to force his way into the Three Lions squad by excelling in more ways than one in United's final three league games.
"You need to do more than score goals to get into the England squad," said Bamford, speaking to BBC West Yorkshire Sport.
"But I've just got to keep trying and do what I can in the last three games and see what happens.
"I have done all I can and I'll keep pushing."
Leeds sit tenth in the Premier League table and will end their first season back in the country's top flight with away clashes at Burnley and Southampton before an Elland Road date against already relegated West Brom on the final day.
Assessing his side's remaining aims, Bamford said: "I think just finish the season strongly.
"We have got to enjoy it.
"It's our first season in the Premier League and we have had a good season but it's making sure that we do finish on a high.
"People in football do have a short term memory.
"They'll say 'Leeds have burnt out again' and it's a load of rubbish but we have got to make sure that we kind of make everyone remember us for a good end to the season as well."
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Thank you Laura Collins