Abraham has had an up-and-down campaign at Swansea since making his season-long loan switch from Chelsea.
The 20-year-old scored five goals by mid-October and that impressive form earned him his first England caps against Germany and Brazil the following month.
New kits: All confirmed and leaked 2018 World Cup strips
Abraham then went 14 games without a goal before scoring twice in Swansea’s record 8-1 FA Cup win against Notts County on Tuesday night – but he revealed England manager Gareth Southgate offered him words of advice back in November.
“After the two games he just said it is going to be tough at Swansea, because of the (league) position you are in,” Abraham said.
“He said just go there and work as hard as you can.
“Just believe in yourself and hopefully get the team out of the mess.”
Abraham scored 26 goals at Sky Bet Championship club Bristol City last season before going out on loan again at Swansea.
It is a similar route to the one taken by England star Kane, who had loan spells at Leyton Orient, Millwall, Norwich and Leicester before flourishing at Tottenham and becoming one of the world’s best strikers.
“He is a player I have always looked up to and he is one of the greatest strikers,” said Abraham, who is hoping for another England call-up for the friendlies with Holland and Italy next month.
“So I obviously follow his past and what he has been through.
“It gives me confidence as well that there is a light at the end of every tunnel, so it encourages me to keep pushing and try my best.
“I would obviously love to go to the World Cup. I have to keep proving myself and that’s what I am willing to do.”
Swansea’s biggest win in 104 years of FA Cup football maintained the feel-good factor at the Liberty Stadium since Carlos Carvalhal’s appointment at the end of December.
The Swans have lost only once in 10 games under Carvalhal and have climbed out of the Premier League relegation zone, as well as progressing into the last 16 of the FA Cup.
Swansea play Burnley next at home on Saturday, a game in which on-loan Leicester midfielder Andy King is expected to make his debut.
“The momentum is the big thing,” Wales international King said.
“We had that when we’ve stayed up at Leicester, you just put a good run of games together and it has a snowball effect.
“I see that here, you’ve just got to stay together as a team, as a squad, and as a city.
“I think that’s going to be big going into the run-in. We’ve got some winnable games at home, and if we can get that right then we’re nearly there.”