Ronald Koeman wants to make Witsel his first marquee signing and Everton have now agreed a fee with his club.
The Toffees are also prepared to match the player’s wage demands with a contract worth over £100,000-a-week.
Napoli were interested in the Belgium midfielder but baulked at the salary he was demanding and have pulled out of the race.
That would appear to leave Everton competing for the 27-year-old’s signature with Chelsea, who have also made enquiries.
Witsel is currently with the Belgium team at Euro 2016 and is expected to start their quarter-final against Wales in Lille tonight.
So any transfer will have to wait until the tournament is over – but sources on Merseyside are confident Everton will get their man.
Koeman has been given a £100m transfer kitty by new investor Farhad Moshiri and sees Witsel as the first of several new signings.
The former Benfica midfielder, who only has a year left on his contract, told Zenit he would only agree to leave for a club in the Champions League.
But Everton have impressed his representatives with their determination to sign him, the ambition of their project and with the size of the financial package on offer.
Moshiri is keen to make a big statement of intent this summer and it is understood he is also about to pay off all of Everton’s bank debt.
The Iranian businessman bought into the club in February and has a deal in place to assume full control. It is believed he will exercise this option in the next few months.
Witsel has scored 21 goals in 156 appearances for Zenit but is part of an exodus of talent expected from the Russian club this summer.
Zenit have already sold Brazil striker Hulk to Chinese Super League side Shanghai SIPG for £45m but further sales are likely.
Witsel has been described as Belgium’s most important player, with coach Marc Wilmots once saying of him: “Axel makes the other players better.”
Chelsea turned their attention to him after becoming frustrated in their pursuit of his countryman Radja Nainggolan.
Roma have been digging their heels in over Nainggolan and have so far rejected all of Chelsea’s attempts to sign him.
It is still possible Chelsea could match Everton’s bid for Witsel, but it is understood Nainggolan remains their first-choice option and they have not yet given up on signing him.
Witsel, who wears the no.6 shirt at Euro 2016 is enjoying a productive tournament in France. He was named man of the match after scoring in Belgium’s 3-0 win over the Republic of Ireland.
He has played every minute of every game as the Belgians, one of the pre-tournament favourites, go in search of a place in the semi-finals.
Witsel began his career with Standard Liege before moving to Benfica in 2011 and to Zenit a year later.