@Chhotu I think we can implement merge sort inplace using linked list. For merging we can do it in O(nlogn), see this: http://www.geeksforgeeks.org/merge-two-sorted-lists-place/
One change is in the sort procedure where we need to find the middle element, when using arrays we can simply find it in O(1). But in linked list it will take O(n). I think that won't affect the recursive equation. http://www.geeksforgeeks.org/merge-sort-for-linked-list/
In general merge sort is not considered in-place sorting technique. Because an auxiliary array is used. If we will try to do it in-place in array data structure then our merge procedure will take O(n2) time. so overall complexity will become not O(n2log2n) but O(n2) . only merging time will increase.
Thank You @VS ji. I waiting for other users reply. Please use latex for formula's for writing answer because it may confuse for other users (like n2)