Unlike other religions, Islam teaches its followers to resort directly to Allah without any intermediary or intercessor. The verse mentioned in the question affirms this principle; it tells us that Allah is near and close to each person, and accordingly there is no need for any external link between servants and Him.
Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: While explaining the Qur’an we should follow the proper methodology. We should understand it as the people who were its first addressees understood it. Qur’anic terms and concepts should be explained by reference to their usages and explanations. Otherwise, we will end up distorting the text, projecting our subjective ideas into them. The result would be the tarnishing the purity of the religion.

The verse, (If My servants ask you about Me, tell them I am near, ready to answer those who call upon Me?) (Al-Baqarah 2: 186) was revealed in an answer to a question put to the Prophet: ‘Tell us about our Lord – is He near that we can whisper to Him, or is He far that we ought to raise our voices?
The verse teaches us that Allah is near and close to each person. There is no need to raise one’s voice while calling upon the Lord. By implication it rules out the need for any intercessor or intermediary. Because Allah is near, each one can speak to Him directly.
It is, therefore, absolutely wrong to state that the above verse refers to the idea that one can come to Allah through Prophet Muhammad (peace and blessings be upon him). Islam teaches us that although Prophet Muhammad is the last Prophet and Messenger, he is not considered an intermediary between man and Allah.