Kemp enters the weekend set third in the National League in batting (.326) behind Milwaukee's Ryan Braun (.330) and New York's Jose Reyes (.329), one back of St. Louis' Albert Pujols (37) for the home run lead, and has a league- high 118 RBI.
"The chants of MVP are overwhelming," said Kemp. "If it happens it happens. I'm not going to put any more pressure on myself."
Boston's Carl Yastrzemski was the last player to lead the league in average, home runs and RBI, while there hasn't been an NL Triple Crown winner since Joe Medwick accomplished the feat for St. Louis in 1937.
Kemp helped his cause on Thursday, as he went 4-for-5 and scored three times in the Dodgers' 8-2 win over San Francisco.
"Six more games, I'm not going to put any more pressure on myself," said Kemp, who has also stolen 40 bases. "I'm just going to hit the ball hard and we'll see where it goes."
The Dodgers won for the 21st time in their last 29 games on Thursday.
Tonight, Los Angeles will rely on lefty Ted Lilly, who has won three of his last four decisions. Lilly beat the Pittsburgh Pirates on Saturday, holding them to a run and four hits in seven innings, as he improved to 10-14 to go along with a 4.27 ERA.
Lilly has faced the Padres 16 times (15 starts) and is 9-4 with a 2.86 ERA against them.
San Diego, meanwhile, will counter with lefty Wade LeBlanc, who is 4-5 with a 5.07 ERA. LeBlanc won for the second straight time after a three-start losing streak on Saturday against Arizona, holding the Diamondbacks to a run and four hits in six innings.
LeBlanc, though, is just 1-5 lifetime versus the Dodgers with a 5.21 ERA in seven starts.
San Diego enters this weekend's set following a three-game sweep of the Colorado Rockies. The Padres have won five of their last six, but still occupy the cellar of the National League West, two games back of the Dodgers.
Los Angeles has owned the Padres this season, going 11-4 against them, including wins in four of the six meetings in San Diego.