Neville, who took over as coach of the ambitious Singapore-owned club when Nuno Espirito Santo was sacked last month, has overseen four draws and two defeats in La Liga ahead of Sunday's trip to Deportivo La Coruna.
Vicente played for Valencia during a golden period between 2000 and 2011, when they twice won La Liga as well as the UEFA Cup and the King's Cup, and has joined the technical staff of sporting director Jesus Garcia Pitarch.
The 34-year-old former Spain international retired from playing in 2013 after a brief stint with English club Brighton. He scored three goals in 38 appearances for Spain, with his last match for La Roja coming in 2005.
"I am really excited to get started and see if I can help the team," Vicente said on Wednesday.
"The fans should stay calm even though the results are not there just at the moment," he added. "I think with patience the victories will come and we can climb up the table."
Unless they can rapidly string a run of wins together, Valencia risk missing out on a lucrative berth in continental competition for next season, the least they would have expected before the start of the campaign.
Valencia, who are in the last 32 of the Europa League and play their King's Cup quarter-final, first leg at home to Las Palmas later on Thursday, are 11th on 24 points from 20 matches, nine points off the European qualification places.
Champions Barcelona, who have a game in hand over their main rivals, can climb above Atletico Madrid to the top with a win at Malaga on Saturday.
Atletico host Sevilla on Sunday, when Real Madrid, two points behind Barca in third, play at Sevilla's city neighbours Real Betis.
Barca will have Luis Suarez available after the Uruguay striker, La Liga top scorer with 18 goals, was suspended for Wednesday's 2-1 Cup victory at Athletic Bilbao.
Lionel Messi remains a doubt, however, after he missed the clash at Bilbao's San Mames stadium due to lingering discomfort following the 6-0 La Liga win at home to the Basque club last weekend.
(Writing by Iain Rogers, editing by xxxxxxxxx)
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