Vucinic is thought to be of interest of the Premier League pair – with the duo both looking to add to their striking ranks this summer – but Valencia are also keen to bring the Montenegrin to Spain.
The striker is currently at Juventus, but the Italian giants are keen to cash-in on the attacker and he could be available for a fee of £6.5million.
The 28-year-old found first-team opportunities hard to come by last season, with Carlos Tevez and Fernando Llorente being the club’s regular strike partnership.
Vucinic made just 19 appearances in all competitions, and could only score two goals, leading to him being put up for sale by Juventus.
Valencia would ordinarily not have posed much of a threat to Arsenal and Tottenham, with the London duo previously able to out-muscle them financially.
However, the La Liga side have recently been the subject of a takeover bid from Peter Lim, a Singaporean millionaire and now have the money to compete with the Premier League pair.
It would be a blow for either Spurs or Arsenal to miss out on the signing of Vucinic, as he is a player who could seriously add to the quality of both sides' front-lines.
Spurs are looking for an attacker to provide the threat that they were desperately lacking in forward positions last seasons, after Roberto Soldado failed to provide the goals that were expected of him following his big-money transfer.
Soldado fell behind Emmanuel Adebayor and Harry Kane in the pecking order last campaign and new manager Mauricio Pochettino has reportedly made signing a striker one of his top priorities since taking charge.
Meanwhile, Arsenal are also on the hunt for an attacker to provide competition for Olivier Giroud.
The Frenchman was a mainstay in the Gunners' side last season, making 56 appearances, largely due to a lack of other options, and Arsene Wenger is said to be keen to bolster his options up-front for the upcoming campaign.