Liverpool have made an impressive start to the season, scoring 12 goals in their opening five games and conceding just once.
Dyche's success with Burnley, who are playing in the Premier League for a sixth consecutive season, had led to speculation of a move.
Townsend previously played under Benitez at Newcastle and displayed his ability to do something spectacular with a long-range effort that looped over Nick Pope into the top corner.
Klopp used a news conference ahead of Liverpool's match against Burnley on Saturday to question whether goalkeepers were being protected enough.
Jordan Pickford has been recognised as England's number one for the past few years but Pope, 29, started all three games in the recent international break.
Euro 2020: England goalkeeper Nick Pope to undergo ‘minor surgery’ on injured knee, doubtful for continental event
Pope was likely to be England's second-choice goalkeeper behind Jordan Pickford at Euro 2020.
Premier League: Liverpool move into top-four after win over Burnley; Tottenham's Europe hopes dented
Jurgen Klopp's side moved into fourth place in the Premier League thanks to goals from Roberto Firmino, Nathaniel Phillips and Alex Oxlade-Chamberlain.
The Hammers are now five points adrift of the top four with just six left to play for after two late goals at the Amex Stadium.
Leeds punished Burnley after the break as Jack Harrison added a second before providing the two assists as Rodrigo came off the bench to bag a brace.
European football matchday: Chelsea meet Leicester City in FA Cup final; Juventus face Inter Milan in bid for top-four
Here's a look at what's happening in European football on Saturday.
Fulham joined West Brom and Sheffield United in being relegated from the Premier League following a 2-0 loss to Burnley on Monday.
Fulham's defeat also meant all three relegation places were decided with at least three games to go, ensuring there would be no last-day drama in the battle to beat the drop.
The result takes Manchester United to 67 points after 33 games, 10 points behind champions-elect Manchester City but eight points clear of third-placed Leicester.
Premier League: Joe Willock’s late equaliser helps Newcastle hold Tottenham to 2-2 draw; Southampton beat Burnley
Jose Mourinho's side were just five minutes away from moving into fourth place when Willock equalised at St James' Park.
John Stones opened the floodgates before an emphatic finish from Gabriel Jesus and Sergio Aguero's first Premier League goal for 14 months from the penalty spot round off the scoring.
European football matchday: Chelsea travel to Leeds United; Bayern Munich at Bremen in most-contested fixture
Chelsea are in the fourth Champions League spot, two points ahead of West Ham, who have a game in hand.
Premier League: Leicester move to second after win over Brighton; Arsenal's top-four hopes fade after loss at Burnley
Depleted by a series of injuries to key players, Leicester have looked fatigued in recent weeks and fell behind after 10 minutes when Adam Lallana swept home his first Brighton goal.
Premier League: Manchester United lose ground on leaders City with fog-bound Crystal Palace draw, Burnley hold Leicester
The stalemate at a foggy Selhurst Park was United's third successive goalless draw in all competitions ahead of Sunday's Manchester derby against City, who are on a record-breaking 21-game winning streak.
European football matchday: Barcelona host Sevilla in semi-finals of Copa del Rey; Ibrahimovic-less AC Milan play Inter
A look at what’s happening in European football on Wednesday
Premier League: Arsenal impress with comeback win against Leicester, Gareth Bale stars as Tottenham beat Burnley
The defeat left Leicester in third place, trailing leaders Manchester City by 13 points with 12 games remaining.