They have joined Paris Saint-Germain, Manchester United and Arsenal in the race for the Netherlands international.
West Ham are open to offers for Summerville as they must raise funds following their relegation to the Championship. They value him at €50 million.
Summerville impressed for West Ham last term, bagging seven goals and five assists across all competitions.
He has carried that form into the World Cup, scoring two goals in two games for the Netherlands.
The 24-year-old should prioritise a move to Villa as he stands a better chance of playing regularly there than at Arsenal, United or PSG.
He would also play regularly at Spurs, but they will not feature in next season’s Champions League and have struggled in the past two seasons.
Villa need attacking reinforcements. Jadon Sancho will leave after the expiration of his loan deal, while Donyell Malen, Leon Bailey and Morgan Rogers have been linked with moves away.
Summerville would give Unai Emery’s side directness, explosive pace and close control, making him a genuine threat against both low-block and attack-minded teams.
His ability to play anywhere across the frontline would allow Emery to rotate and change tactics during games.
Villa are also exploring a move for PSG youngster Ibrahim Mbaye, but his lack of experience makes him a risky signing.
They have also been linked with Harvey Barnes, but Newcastle United would demand a significant fee for him.
Stats from sofascore.com.