The Northampton director of rugby is widely regarded as the leading candidate, having guided the Saints from the second division to last season's Heineken Cup final in just three years.
Nick Mallett and Graham Henry, two options with international coaching experience, appear to have ruled themselves out of contention.
Mallinder initially expressed his interest in the England job three weeks ago, while Johnson was still deciding whether to continue in the wake of a disappointing World Cup campaign.
With the position now officially vacant, Mallinder has reiterated his desire to be considered for the job of coaching England into the 2015 World Cup on home soil.
But he confirmed there had been no official contact with Northampton from the Rugby Football Union.
"I have said a few weeks ago that everybody strives to be the best they can and coaching the national side is a massive honour," Mallinder said.
"I have said previously that it is (a role that interests me).
"There have been no questions asked and at this moment I am very happy and I think I have got a really important job to do, getting this side (Northampton) back up and winning rugby matches."
Mallinder was speaking after the Saints suffered a 28-23 home defeat to the Scarlets, which leaves them facing the very real prospect of early elimination from the Heineken Cup.
Northampton opened their campaign with a last-gasp defeat to Munster last weekend.
Mallinder said: "It was always going to be tight, every game very competitive. To lose our first two games is a massive blow to our aspirations of getting through this year.
"We will look at ourselves. We were very disappointing in a lot of areas. We played badly and deserved to come second."
The Scarlets, who opened their campaign with a victory over Castres, had the game wrapped up by half-time with tries from Liam Williams, Aaron Shingler and Matt Gilbert.
Rhys Priestland, the Wales fly-half making his first start since the World Cup, scored the bonus-point try as the Scarlets counter-attacked following a Chris Ashton knock-on.
The Saints staged a late comeback to earn a losing bonus point with tries from George Pisi and Tom Wood, on top of 13 points from Ryan Lamb.
The Scarlets top Pool One with nine points and are in a strong position to reach the knockout stages.
"We had to play a very good game of rugby to get a result here and that is what we did," said Scarlets boss Nigel Davies.
"This is pretty big against a side of Northampton's quality. I don't think they have lost a European encounter at home since 2007 so it is a big scalp for us.
"We have to build the momentum. The big thing has been belief, believing we can come to places like this."