Q:

Can micro black holes form in the Sun?

Wikipedia writes to say 
Factor (J)     SI prefix    Value           Item

10E−7            nJ        5.6×10E−7 J     energy per proton in the CERN Large  
                                           Hadron Collider in 2011 (3.5 TeV)
10E3             kJ        1.4×10E3 J      total solar radiation received from the 
                                           Sun by 1 square meter at the altitude 
                                           of Earth's orbit per second (solar 
                                           constant)

This leads to the assumption the energy generated at Sol's core is significantly higher. 
If this assumption is correct, and the earlier reports in media about creation of micro-black-holes in more powerful avatars of LHC are reasonable, would it be far-fetched to state micro-black-holes may form within a star too?

A:

This leads to the assumption the energy generated at Sol's core is significantly higher.

High energy interactions of particles implied in the phenomenological models of the creation of micro black holes are a function of the energy of the individual particles .
Individual particles are accelerated to the TeV energies of the LHC, each single proton. In the sun the average energy of individual particles is very low, in the nuclear regime, which is about a million times lower than a TeV. 

If this assumption is correct, and the earlier reports in media about creation of micro-black-holes in more powerful avatars of LHC are reasonable, would it be far-fetched to state micro-black-holes may form within a star too?

The assumption is not correct because it confuses the total luminosity per square meter coming from the sun with the energy of the individual particles which compose this radiance.
In this lecture the reactions that generate the luminosity of the sun are calculated, and give 27 MeV on average for the particles available for further interactions particle on particle. Everything starts with hydrogen on hydrogen.

So except for the energy given to the neutrinos, which exit the star
  without depositing any energy, the 27 MeV is available to provide the solar
  luminosity. 

This is too low for any phenomenological model of micro black holes by a million in order of magnitude.
There do exist higher energy particles coming from the corona of the sun accelerated by the magnetic fields, the tail end even in GeV and are part of the cosmic radiation environment around earth, but still the energy is very low.
Cosmic rays are our first and maybe our final laboratory creating high energy particles, but they come from the galaxy and the cosmos. The tail end of their energy distribution has particles with energy immensely  greater than the ones we can ever generate on earth.
It was the main argument that refuted the fear mongering assumption that the earth might be in danger of micro black holes  created at the LHC! Much higher energy interactions in our atmosphere have not destroyed the earth yet over the billions of years it exists :).

