After captaining England to nine victories in a row this year, Hartley is favourite for the Lions job in 2017.
But after meeting for a short camp last weekend, Hartley insists all the focus is on England's November opener against South Africa.
"Every player has that in the back of their mind," Hartley told BBC Sport.
"Lions selection comes off the back of playing well for your country, so at the moment everyone's focus should be on playing well for their clubs and getting picked for England.
"You are always judged on your next performance, so I just want to play well for my club and be in [the frame for] selection for that South Africa game in November."
England face South Africa, Fiji, Argentina and Australia in successive weekends in the autumn, and can go through 2016 unbeaten if they avoid defeat.
"The key message from Eddie is how as a team do we get better, how do we improve?" Hartley added.
"Without winning that first game there is no point talking about going unbeaten, [so] every meeting we have had these last few days has been about South Africa and building for that game.
"I don't think anyone in our team has beaten South Africa before, so there's a huge opportunity there for us as a group."
Meanwhile, Hartley believes the new club and country agreement will be of great benefit to the national side.
Under terms of the new deal between the RFU and the Premiership clubs, which was finalised last month, England coach Eddie Jones will have more regular access to his players.
A 45-man group assembled in Teddington last weekend, a matter of weeks after the successful tour of Australia in June.
"We have a couple more of these camps before [the matches in] November which keeps us all connected and in England mode," Hartley said.
"It's hard to go from club to England, so the more we can meet together as a group the better for us as a team.
"It keeps us tighter as a group, and the more we meet those bonds stay tight."

At least one bomber blew himself up outside the mausoleum of Sayid Mohammed bin Ali al-Hadi, which was then stormed by gunmen, reports say.
Another bomber is said to have blown himself up among fleeing worshippers.
Meanwhile the death toll from Sunday's suicide bombing in Baghdad has again been raised, from 281 to 292.
Amid growing public anger over the truck bombing, Iraqi Prime Minister Haider al-Abadi fired the three top security officials in Baghdad on Friday.
They were the head of Baghdad's security command, the head of interior ministry intelligence for Baghdad and the official responsible for Baghdad in the national security adviser's office.
IS said five of its members had carried out the raid on the site in Balad. The militant group follows an extreme form of Sunni Islam and often targets Shias, who it regards as apostates.
About 50 people were injured in the attack, police and medical sources said.
Islamic State: The full story
Worshippers were marking the Eid al-Fitr festival, celebrating the end of the Islamic holy month of Ramadan, when the site came under mortar fire.
The first bomber then struck a market at the entrance to the shrine.
A third bomber was shot dead before he was able to detonate his explosive vest, reports say.
It came four days after IS carried out the deadliest bombing in Baghdad, 45 miles (70km) south of Balad, since the 2003 US-led invasion.
That attack target a shopping complex in the mainly Shia Muslim district of Karrada.
IS militants overran large parts of northern and western Iraq two years ago, but government forces have since regained much of the territory.
In response to the battlefield setbacks, including the recent loss of the western city of Falluja, the militants have stepped up their attacks on civilians.
The Iraqi government has been accused of not doing enough to protect its citizens and has stepped-up security in Baghdad in response to the latest violence.
England skipper Dylan Hartley has urged his players not to become pre-occupied with the British and Irish Lions tour of New Zealand next summer.
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Suicide bombers and gunmen have killed at least 35 people in an attack by so-called Islamic State (IS) at a Shia shrine in the Iraqi town of Balad.