Twelvetrees' place in the starting XV was under threat after he struggled within a misfiring centre partnership alongside Joel Tomkins in the weekend's 20-13 victory over Australia.
The Gloucester back, winning his sixth cap, was at fault for the Wallabies' try after being brushed aside by Matt Toomua and finished as one of England's worst-performing players.
Northampton's Luther Burrell has been the Aviva Premiership's form centre and is pressing Twelvetrees hard, but Lancaster refuses to wield the axe on the strength of one display.
"Billy is disappointed with one or two areas of his game, but a lot of areas were pretty good. We have to give him credit for that," Lancaster said.
"We'll make the decision over the next 24-48 hours, but I'm not envisaging too many changes.
"There is definitely scope to make changes. Luther Burrell and Kyle Eastmond are obvious inside centre options and Henry Trinder an outside centre option.
"But Billy's done pretty well for us and deserves another chance I think."
Tomkins also endured a mixed afternoon on his debut, but both centres suffered amid a disjointed backline that spluttered throughout the autumn opener at Twickenham.
Lancaster is reluctant to judge the duo solely on their shifts against Australia, but accepts there is work to be done in the combination.
"They didn't have a huge amount of opportunities," he said. "I know Billy's a bit disappointed about missing his tackle, but overall he had a solid game.
"Joel did well in his first international. There's definitely more in us and we feel we can improve in that area, but overall it's pretty positive."
Alex Corbisiero is set to return against Argentina after recovering from his knee injury.
If the Northampton loosehead starts as expected, Mako Vunipola will be displaced to the bench even though he impressed against the Wallabies, who were demolished at the scrum.
Lock Geoff Parling has been given the all-clear from the concussion incurred in training last week and is available for selection.
Vunipola, Tomkins, Trinder, Marland Yarde and Tom Wood have minor knocks, but no player has been ruled out of the second QBE International.
Argentina are the weakest opposition of the autumn after finishing bottom of the Rugby Championship, but Lancaster still views them as formidable opponents.
England swept aside a weakened Pumas team over two Tests during the summer and are targeting their ninth win in 10 matches.
"Having played Argentina in the summer, we found them pretty difficult to break down, particularly in the second Test," he said.
"Their performances in the Rugby Championship have shown that on their day they can push the top two or three teams in the world very close.
"We'll take them on merit and give them the credit they deserve as a proud rugby playing nation.
"But we won't concentrate on Argentina until the end of the week."