While Pekerman is unsure regarding any speculation, he knows very well that the 30-year-old striker has to recover from his current injury woes and put together a consistent run if he is to play a part for Los Cafeteros at Copa America 2016 which kicks off in the USA in early June.
"I talk to him, but always with the expectations and desire for a healthy recovery, that's the most important thing. If he's not well, it would be very difficult for him to recover his competitive level," said Pekerman.
"We have many players who need to recover their playing time, and we need to focus on the generational shift that Colombia needs, and hopefully Falcao can be part of that."
Regarding the Columbus links, Pekerman said: "I didn't know about Columbus' interest, but a lot of teams want Falcao, and hopefully he starts playing again soon.
"He's soon to recover from his latest injury and might come back with Chelsea any time. But wherever it is, it's important that he gains his confidence and playing time back."
And when addressing reports that former Atletico Madris star Falcao was prepared to consider MLS over China, Pekerman added further: "Each one is free to choose what they want for their future, but for the national team it's an inconvenience [to play in China] because of the long distances of travel.
"Not because of their quality, because they can train and compete well anywhere they are, but because trips will be longer and they'd have less days to recover. It's a difficulty."