Hodgson admits he may have to dash the World Cup dreams of some of his senior England players, having chosen a number of inexperienced names in his 30-strong squad for next week's friendly against Denmark.
While Hodgson has not directly named those he might think to leave behind, it would be reasonable to assume players like Cole and Lampard, who have over 200 caps between them, are under threat.
Cole has been a mainstay of tournament football for England since 2002, but the 33-year-old left-back is no longer first choice at Chelsea, with Southampton's Luke Shaw likely to get the nod against the Danes.
Lampard - who turns 36 in late June - would probably be looking at a last World Cup finals appearance this year, and was England's second top-goalscorer in the qualifying campaign.
Hodgson is set to name his provisional squad on May 13, which will eventually be trimmed down to 23.
Mourinho is in no doubt his Chelsea duo should be on the plane.
"It is not my decision, but I try to be pragmatic, so if one day I am the national team manager of any country, I think the players that take me to the Euros or to the World Cup are the players I am going to take to the Euros or the World Cup," the Portuguese coach said.
"They took me, by qualifying, so after that, I take them on my plane.
"I don't think it makes a lot of sense if you trust some players to do qualification and, after that, you don't select them and pick others."
Mourinho was a potential candidate to succeed Steve McClaren as England manager in 2007.
The Chelsea boss claims if he did eventually move into international management, he would not be keen on selecting players via naturalisation - as could be the case with Manchester United's Belgium-born Kosovan midfielder Adnan Januzaj.
"When, one day I am a national coach, I will take only players born in my country, that is for sure, or if not born in my country, then with parents with a big connection with the country," Mourinho said.
"I will never take a player just because he has a passport from my country thinking he can make my team stronger.
"For me, the national team means a lot, my national team means a lot.
"If, one day, I coach Portugal, I will go with the Portuguese. The national team is Portugal. It's not Portugal & Friends. Portugal is for the Portuguese.
"It is an option, and anyone is free to have his options, and I'm not criticising, I am just saying (what I would do) when I am a national coach - and normally that would be the Portuguese national coach."
Mourinho also suggested he would rather managers also come from their own countries.
"(Overseas national coaches) can be allowed, but if I was a president of a federation, maybe the Portuguese Federation, then Portuguese managers - but everything is 'supposed'," he added.