Silva is some bookmakers' third-favourite to replace Ronald Koeman at Everton bu insists he's happy at Watford.
Dyche is seen as one of the frontrunners to succeed Ronald Koeman, but members of the Everton squad want David Unsworth to be handed the role permanently.
Teenage midfielder Beni Baningime played 90 minutes of Everton's Carabao Cup fourth round defeat to Chelsea on Wednesday after Morgan Schneiderlin was taken ill.
Ronald Koeman failed to sign an adequate replacement for Romelu Lukaku, who left Everton to join Manchester United in the summer.
Henen, a pacey forward, joined Everton in the summer of 2014 but has not yet made a first-team appearance for the Toffees.
Chelsea star N'Golo Kante is edging closer to making a return to action from the hamstring injury he sustained during the recent international break.
The Merseysiders were interested in signing Costa in the summer but the fiery Spaniard eventually returned to Atletico Madrid.
Everton host Chelsea in the Carabao Cup fourth round in what is David Unsworth's first match in charge following Ronald Koeman's departure.
Chelsea and Everton battling to reach the last eight of the Carabao Cup amid differing managerial situations.
Everton were believed to be interested in signing Dost when Ronald Koeman was in charge at Goodison Park.
David Unsworth could use his second spell in caretaker charge of Everton but handing debut to two of his Under-23 side in the Carabao Cup against Chelsea.
Barkley is widely expected to leave his boyhood club in the coming months but Unsworth is hopeful he can change his mind.
Unsworth has been appointed as caretaker manager at Goodison Park but has made no secret of his desire to be put in permanent control.
Koeman was relieved of his duties on Monday after overseeing a dreadful start to the new campaign on Merseyside.
Unsworth will lead the Toffees against Chelsea on Wednesday (25 October) and will also be in control for the games against Leicester City, Watford and Lyon.
Everton sacked Ronald Koeman on Monday after a disastrous run of results left the team in the bottom three.
Ryan Giggs has been out of management after Louis van Gaal was allowed to leave Manchester United after the end of the 2015/16 season. The Dutchman was replaced by Jose Mourinho.
Graham Stuart says Everton have failed to find ways to replace Romelu Lukaku's goals. The Belgium international left the Toffees to join Manchester United.
Wingers Charly Musonda Jr and Kenedy are both set to feature for Chelsea during Wednesday night's Carabao Cup fourth round clash against managerless Everton.
Everton have announced the departure of under-fire boss Ronald Koeman following a 5-2 defeat to Arsenal that left them in the Premier League relegation zone.
Mesut Ozil, Alexandre Lacazette and Alexis Sanchez all score in thumping win at Goodison Park.
Former Everton captain Neville thinks Koeman can turn his side's ailing fortunes around and will be given the chance to do so by Bill Kenwright.