How to "cultivate" a postdoc position during PhD program?
You want to establish substantial professional contact with the head of your target group long before your doctoral period is about to end.  They need to know who you are already when your postdoc application crosses their desk.  It is never too early to start.  Here are a few suggestions.


Ask your advisor to invite the head of the group to give a talk in your department.  Meet with them one-on-one.  Ask about the possibility of a short visit to their lab to give a reciprocal talk.  (Prerequisite: Have something compelling to talk about; be a good speaker.)
Ask about the possibility of summer internships.  (Prerequisite: Be a good candidate for a summer internship.)
Ask your advisor to suggest a one-semester student swap.  (Prerequisite: Be someone that the other person would want to hire as an RA.)  More generally: Convince your advisor to collaborate with the other group.
Ask the head of the group to be an external member of your dissertation committee.  Ask at least two years before your defense. (Prerequisite: Have a thesis topic that they will care about.)
Talk to the head of the group and/or his students at conferences.  Join them for lunch, or dinner, or coffee, or beer, or whatever.  (Prerequisite: Be an interesting human being.  Know a few good places to get lunch/dinner/coffee/beer/whatever.)
Don't put all your eggs in one basket.  Cultivate multiple colleagues.  Some may develop into future employers, others into future research collaborators, still others into letter-writers, still others into mentors,  perhaps a few into friends, and most into nothing.  (Prerequisite: Know more than one person.)
Most importantly, don't think of this process primarily as "cultivating a postdoc position".  Think of it as cultivating a research community.  People will notice if your motivations are mercenary, if only subconsciously.