Sven-Goran Eriksson's right-hand man wants a quick decision on the Swede's future - but says he must only be sacked for footballing reasons.
The Football Association was forced to confirm Eriksson had an affair with secretary Faria Alam, five days after denying the relationship happened.
Now there will be an inquiry and Grip told BBC Five Live: "They must go out and tell him and be very straight.
"They must say 'okay, you should not be here any longer.'"
Grip added: "They should do that but not for something done wrong in his private life but for something done wrong with the national team."
FA executive director David Davies has welcomed the decision to hold an inquiry into the handling of Sven-Goran Eriksson's reported affair.
The FA was forced into an embarassing U-turn when it confirmed Eriksson had an affair with secretary Faria Alam, five days after denying this was true.
"I'm delighted the chairman Geoff Thompson has initiated the investigation," said Davies.
"I will contribute over the next few days," he added.
It is believed the inquiry will focus on whether Eriksson lied to the FA about the affair before the initial, incorrect statement was released.
Eriksson, in line with his policy of never commenting on his private life, has insisted he never confirmed nor denied having an affair with Alam at any point.
The FA board will discuss the matter at a hastily-convened meeting on Thursday.
Davies, who has returned from holiday to take part in the inquiry, said: "I am upset by some of the tone and content of things I have heard and read while I have been away.
"The quicker we get the matter resolved the better and then everyone gets back to doing what they are there for and that is giving the players the best chance of being successful."
Davies would not comment on Eriksson's future - but said the Swede had the full backing of the FA while the investigation was ongoing.
"Sven is England coach. He has a long-term record of success in various countries in Europe which everyone quite rightly respects him for that and will continue to do so.
"Everyone knows the support the FA have given Sven and I regret very much we
are dealing with this incident at the moment."